Publications

Books

Follow this link to read Ivan's unfinished online book "Introducing ordered sets: Lectures on Ordered Sets".

Essays

In addition to "Picture Puzzling" Ivan published a number of other essays on mathematics in non-specialist journals. We are still in the process of identifying these articles, locating them and preparing them for web publication. We will post the full text of these articles when they are ready.

I. Rival. Picture puzzling: mathematicians are rediscovering the power of pictorial reasoning. The Sciences. New York Academy of Sciences: January/February 1987, 40-46.

Workshops

I.Rival (1991) Order aspects of ice flow, Workshop Combin. Optimiz. Sci. Tech. (E.Boros, P.L.Hammer, eds.), Rutgers, 286-289.

Scientific Publications

The following is a (possibly incomplete) list of Ivan's books edited, chapters in books, papers in refereed journals and papers in refereed conference proceedings.

[1] Alzohairi, Mohammad; Rival, Ivan; Kostochka, Alexandr The pagenumber of spherical lattices is unbounded. Arab J. Math. Sci. 7 (2001), no. 1, 79--82.

[2] Lee, Jeh Gwon; Liu, Wei-Ping; Nowakowski, Richard; Rival, Ivan Dimension invariance of subdivisions. Bull. Austral. Math. Soc. 63 (2001), no. 1, 141--150.

[3] Hashemi, S. Mehdi; Rival, Ivan; Kisielewicz, Andrzej The complexity of upward drawings on spheres. Order 14 (1997/98), no. 4, 327--363.

[4]ORDAL '96. Papers from the Conference on Orders, Algorithms and Applications held at the University of Ottawa, Ottawa, ON, August 5--9, 1996. Edited by I. Rival and N. Zaguia. Theoret. Comput. Sci. 217 (1999), no. 2. Elsevier Science Publishers, B.V., Amsterdam, 1999. pp. i--iv and 173--436.

[5]Grätzer, George; Rival, Ivan; Zaguia, Nejib A correction to: "Small representations of finite distributive lattices as congruence lattices" Proc. Amer. Math. Soc. 126 (1998), no. 8, 2509--2510.

[6]K. Ewacha, I. Rival and N. Zaguia, 1997, Unimodality, Linear Extensions and Width Two Orders, Discrete Mathematics.

[7]Ewacha, Kevin; Rival, Ivan; Zaguia, Nejib Approximating the number of linear extensions. Orders, algorithms and applications (Lyon, 1994). Theoret. Comput. Sci. 175 (1997), no. 2, 271--282.

[8]Rival, Ivan Order, ice and surfaces. Lattice theory and its applications (Darmstadt, 1991), 211--218, Res. Exp. Math., 23, Heldermann, Lemgo, 1995.

[9]Fofanova, Tatiana; Rival, Ivan; Rutkowski, Aleksander Dimension two, fixed points and dismantlable ordered sets. Order 13 (1996), no. 3, 245--253.

[10]Pouzet, M.; Reuter, K.; Rival, I.; Zaguia, N. A generalized permutahedron. Algebra Universalis 34 (1995), no. 4, 496--509.

[11] Liu, Wei-Ping; Rival, Ivan; Zaguia, Nejib Automorphisms, isotone self-maps and cycle-free orders. Combinatorics of ordered sets (Oberwolfach, 1991). Discrete Math. 144 (1995), no. 1-3, 59--66.

[12]Grant, Ken; Nowakowski, R. J.; Rival, Ivan The endomorphism spectrum of an ordered set. Order 12 (1995), no. 1, 45--55.

[13] Rival, I.; Rutkowski, A. Does almost every isotone, self-map have a fixed point? Extremal problems for finite sets (Visegrád, 1991), 413--422, Bolyai Soc. Math. Stud., 3, János Bolyai Math. Soc., Budapest, 1994.

[14] Rival, Ivan; Zaguia, Nejib Perpendicular orders. Discrete Math. 137 (1995), no. 1-3, 303--313.

[15] Rival, I.; Zaguia, N. Images of simple lattice polynomials. Algebra Universalis 33 (1995), no. 1, 10--14.

[16] Hashemi, S. Mehdi; Rival, Ivan Upward drawings to fit surfaces. Orders, algorithms, and applications (Lyon, 1994), 53--58, Lecture Notes in Comput. Sci., 831, Springer, Berlin, 1994.

[17] Grätzer, George; Rival, Ivan; Zaguia, Nejib Small representations of finite distributive lattices as congruence lattices. Proc. Amer. Math. Soc. 123 (1995), no. 7, 1959--1961.

[18] Fon-Der-Flaass, Dmitri; Rival, Ivan Collecting information in graded ordered sets. Parallel Process. Lett. 3 (1993), no. 3, 253--260.

[19] Rival, Ivan Problems about planar orders. Finite and infinite combinatorics in sets and logic (Banff, AB, 1991), 337--347, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 411, Kluwer Acad. Publ., Dordrecht, 1991.

[20] Kisielewicz, Andrzej; Rival, Ivan Every triangle-free planar graph has a planar upward drawing. Order 10 (1993), no. 1, 1--16.

[21] Rival, Ivan Reading, drawing, and order. Algebras and orders (Montreal, PQ, 1991), 359--404, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 389, Kluwer Acad. Publ., Dordrecht, 1993.

[22] Rival, Ivan; Urrutia, Jorge Representing orders by moving figures in space. Algebraic graph theory (Leibnitz, 1989). Discrete Math. 109 (1992), no. 1-3, 255--263.

[23] Nowakowski, Richard; Rival, Ivan; Urrutia, Jorge Lattices contained in planar orders are planar. Algebra Universalis 29 (1992), no. 4, 580--588.

[24] Rival, Ivan; Stanford, Miriam Algebraic aspects of partition lattices. Matroid applications, 106--122, Encyclopedia Math. Appl., 40, Cambridge Univ. Press, Cambridge, 1992.

[25] Foldes, Stephan; Rival, Ivan; Urrutia, Jorge Light sources, obstructions and spherical orders. Discrete Math. 102 (1992), no. 1, 13--23.

[26] Ewacha, Kevin; Li, Wei Xuan; Rival, Ivan Order, genus, and diagram invariance. Order 8 (1991), no. 2, 107--113.

[27] Liu, Wei-Ping; Rival, Ivan Enumerating orientations of ordered sets. Combinatorics of ordered sets (Oberwolfach, 1988). Discrete Math. 88 (1991), no. 2-3, 239--247.

[28] Czyzowicz, Jurek; Pelc, Andrzej; Rival, Ivan Planar ordered sets of width two. Math. Slovaca 40 (1990), no. 4, 375--388.

[29] Czyzowicz, Jurek; Rival, Ivan; Urrutia, Jorge Galleries and light matchings: fat cooperative guards. Vision geometry (Hoboken, NJ, 1989), 21--28, Contemp. Math., 119, Amer. Math. Soc., Providence, RI, 1991.

[30] Czyzowicz, J.; Pelc, A.; Rival, I.; Urrutia, J. Crooked diagrams with few slopes. Order 7 (1990), no. 2, 133--143.

[31] Quackenbush, R. W.; Rival, I.; Rosenberg, I. G. Clones, order varieties, near unanimity functions and holes. Order 7 (1990), no. 3, 239--247.

[32] Al-Thukair, Fawzi; Pelc, Andrzej; Rival, Ivan; Urrutia, Jorge Motion planning, two-directional point representations, and ordered sets. SIAM J. Discrete Math. 4 (1991), no. 2, 151--163.

[33] Czyzowicz, J.; Pelc, A.; Rival, I. Unfolding weighted consensus orders into consistent numerical scales. Topics in combinatorics and graph theory (Oberwolfach, 1990), 207--217, Physica, Heidelberg, 1990.

[34] Reuter, Klaus; Rival, Ivan Genus of orders and lattices. Graph-theoretic concepts in computer science (Berlin, 1990), 260--275, Lecture Notes in Comput. Sci., 484, Springer, Berlin, 1991.

[35] 92c:06003 Pelc, Andrzej; Rival, Ivan Orders with level diagrams. European J. Combin. 12 (1991), no. 1, 61-68.

[36] Liu, Wei-Ping; Rival, Ivan Inversions, cuts, and orientations. Discrete Math. 87 (1991), no. 2, 163--174.

[37] Rival, Ivan Graphical data structures for ordered sets. Algorithms and order (Ottawa, ON, 1987), 3--31, Kluwer Acad. Publ., Dordrecht, 1989.

[38] Czyzowicz, Jurek; Pelc, Andrzej; Rival, Ivan Drawing orders with few slopes. Discrete Math. 82 (1990), no. 3, 233--250.

[39] Di Battista, Giuseppe; Liu, Wei-Ping; Rival, Ivan Bipartite graphs, upward drawings, and planarity. Inform. Process. Lett. 36 (1990), no. 6, 317--322.

[40] Bandelt, Hans-Jürgen; Rival, Ivan Diagrams, orientations, and varieties. Order 6 (1989), no. 2, 119-132.

[41] Nowakowski, Richard; Rival, Ivan; Urrutia, Jorge Representing orders on the plane by translating points and lines. Computational algorithms, operations research and computer science (Burnaby, BC, 1987). Discrete Appl. Math. 27 (1990), no. 1-2, 147--156.

[42] Algorithms and order. Proceedings of the NATO Advanced Study Institute held in Ottawa, Ontario, June 1--12, 1987. Edited by Ivan Rival. Kluwer Academic Publishers, Dordrecht, 1989. x+498 pp. ISBN: 0-7923-0007-6

[43] Pouzet, Maurice; Rival, Ivan Is there a diagram invariant? Proceedings of the Oberwolfach Meeting "Kombinatorik" (1986). Discrete Math. 73 (1989), no. 1-2, 181--188.

[44] Bandelt, Hans-Jürgen; Rival, Ivan Classifying graphs by intersecting disks. J. Combin. Inform. System Sci. 10 (1985), no. 1-2, 41-51.

[45] Nevermann, Peter; Rival, Ivan Holes in ordered sets. Graphs Combin. 1 (1985), no. 4, 339--350.

[46] Rival, Ivan; Urrutia, Jorge Representing orders on the plane by translating convex figures. Order 4 (1988), no. 4, 319--339.

[47] Nowakowski, Richard; Rival, Ivan Retract rigid Cartesian products of graphs. Discrete Math. 70 (1988), no. 2, 169--184.

[48] Rival, Ivan; Zaguia, Nejib Greedy linear extensions with constraints. Special issue: ordered sets (Oberwolfach, 1985). Discrete Math. 63 (1987), no. 2-3, 249--260.

[49] Jawhari, El Moustafa; Pouzet, Maurice; Rival, Ivan A classification of reflexive graphs: the use of "holes". Canad. J. Math. 38 (1986), no. 6, 1299--1328.

[50] Jégou, Roland; Nowakowski, Richard; Rival, Ivan The diagram invariant problem for planar lattices. Acta Sci. Math. (Szeged) 51 (1987), no. 1-2, 103--121.

[51] Rival, Ivan; Zaguia, Nejib Constructing N-free, jump-critical ordered sets. Proceedings of the seventeenth Southeastern international conference on combinatorics, graph theory, and computing (Boca Raton, Fla., 1986). Congr. Numer. 55 (1986), 199--204.

[52] Hell, Pavol; Rival, Ivan Absolute retracts and varieties of reflexive graphs. Canad. J. Math. 39 (1987), no. 3, 544--567.

[53] Reuter, Klaus; Rival, Ivan Subdiagrams equal in number to their duals. Algebra Universalis 23 (1986), no. 1, 70--76.

[54] Rival, Ivan; Zaguia, Nejib Effective constructions of cutsets for finite and infinite ordered sets. Acta Sci. Math. (Szeged) 51 (1987), no. 1-2, 191--207.

[55] Rival, Ivan; Zaguia, Nejib Constructing greedy linear extensions by interchanging chains. Order 3 (1986), no. 2, 107--121.

[56] Lonc, Zbigniew; Rival, Ivan Chains, antichains, and fibres. J. Combin. Theory Ser. A 44 (1987), no. 2, 207--228.

[57] Ginsburg, J.; Rival, I.; Sands, B. Antichains and finite sets that meet all maximal chains. Canad. J. Math. 38 (1986), no. 3, 619-632.

[58] . Rival, Ivan Stories about order and the letter ${\ssf N}$ (en). Combinatorics and ordered sets (Arcata, Calif., 1985), 263--285, Contemp. Math., 57, Amer. Math. Soc., Providence, RI, 1986.

[59] . Combinatorics and ordered sets. Proceedings of the AMS-IMS-SIAM joint summer research conference held at Humboldt State University, Arcata, Calif., August 11--17, 1985. Edited by Ivan Rival. Contemporary Mathematics, 57. American Mathematical Society, Providence, RI, 1986. xvi+285 pp. ISBN: 0-8218-5051-2 06-06.

[60] . Rival, Ivan Some order-theoretical ideas about scheduling. IX symposium on operations research. Part I. Sections 1--4 (Osnabrück, 1984), 419--430, Methods Oper. Res., 49, Athenäum/Hain/Hanstein, Königstein, 1985. 90B35.

[61] . El-Zahar, M. H.; Rival, I. Greedy linear extensions to minimize jumps. Discrete Appl. Math. 11 (1985), no. 2, 143--156. (Reviewer: H. T. Lau).

[62] Rival, Ivan The diagram. Graphs and order (Banff, Alta., 1984), 103--133, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 147, Reidel, Dordrecht, 1985.

[63] El-Zahar, M. H.; Rival, I. Examples of jump-critical ordered sets. SIAM J. Algebraic Discrete Methods 6 (1985), no. 4, 713--720.

[64] Rival, Ivan; Zaguia, Nejib Antichain cutsets. Order 1 (1985), no. 3, 235--247.

[65] Graphs and order. The role of graphs in the theory of ordered sets and its applications. Proceedings of the NATO Advanced Study Institute held in Banff, Alta., May 18--31, 1984. Edited by Ivan Rival. NATO Advanced Science Institutes Series C: Mathematical and Physical Sciences, 147. D. Reidel Publishing Co., Dordrecht, 1985. xix+796 pp. ISBN: 90-277-1943-8 05-06

[66] Rival, Ivan Linear extensions of finite ordered sets. Orders: description and roles (L'Arbresle, 1982), 355--370, North-Holland Math. Stud., 99, North-Holland, Amsterdam, 1984.

[67] Rival, Ivan; Sands, Bill Pictures in lattice theory. Algebraic and geometric combinatorics, 341--355, North-Holland Math. Stud., 65, North-Holland, Amsterdam, 1982.

[68] Rival, Ivan; Sands, Bill How many four-generated simple lattices? Universal algebra and applications (Warsaw, 1978), 67--72, Banach Center Publ., 9, PWN, Warsaw, 1982.

[69] Pouzet, Maurice; Rival, Ivan Quotients of complete ordered sets. Algebra Universalis 17 (1983), no. 3, 393--405.

[70] Pouzet, Maurice; Rival, Ivan Every countable lattice is a retract of a direct product of chains. Algebra Universalis 18 (1984), no. 3, 295--307.

[71] Galvin, F.; Rival, I.; Sands, B. A Ramsey-type theorem for traceable graphs. J. Combin. Theory Ser. B 33 (1982), no. 1, 7--16.

[72] Rival, Ivan Optimal linear extensions by interchanging chains. Proc. Amer. Math. Soc. 89 (1983), no. 3, 387--394.

[73] Nowakowski, Richard; Rival, Ivan The smallest graph variety containing all paths. Discrete Math. 43 (1983), no. 2-3, 223--234.

[74] Nowakowski, Richard; Rival, Ivan On a class of isometric subgraphs of a graph. Combinatorica 2 (1982), no. 1, 79--90.

[75] Duffus, Dwight; Rival, Ivan Graphs orientable as distributive lattices. Proc. Amer. Math. Soc. 88 (1983), no. 2, 197--200.

[76] Rival, Ivan The retract construction. Ordered sets (Banff, Alta., 1981), pp. 97--122, NATO Adv. Study Inst. Ser. C: Math. Phys. Sci., 83, Reidel, Dordrecht-Boston, Mass., 1982.

[77] Pouzet, Maurice; Rival, Ivan Which ordered sets have a complete linear extension? Canad. J. Math. 33 (1981), no. 5, 1245--1254.

[78] Davey, Brian A.; Rival, Ivan Exponents of lattice-ordered algebras. Algebra Universalis 14 (1982), no. 1, 87--98.

[79] Duffus, D.; Rival, I.; Winkler, P. Minimizing setups for cycle-free ordered sets. Proc. Amer. Math. Soc. 85 (1982), no. 4, 509--513.

[80] Ordered sets. Edited by Ivan Rival. Proceedings of a NATO Advanced Study Institute held in Banff, Alta., August 28--September 12, 1981. NATO Advanced Study Institute Series C: Mathematical and Physical Sciences, 83. D. Reidel Publishing Co., Dordrecht-Boston, Mass., 1982. xviii+966 pp. ISBN: 90-277-1396-0 06-06

[81] Rival, I.; Ruckelshausen, W.; Sands, B. On the ubiquity of herringbones in finitely generated lattices. Proc. Amer. Math. Soc. 82 (1981), no. 3, 335-340.

[82] Rival, Ivan; Wille, Rudolf The smallest order variety containing all chains. Discrete Math. 35 (1981), 203-212.

[83] Duffus, D.; Pouzet, M.; Rival, I. Complete ordered sets with no infinite antichains. Discrete Math. 35 (1981), 39--52.

[84] Rival, Ivan The problem of fixed points in ordered sets. Combinatorics 79 (Proc. Colloq., Univ. Montréal, Montreal, Que., 1979), Part I. Ann. Discrete Math. 8 (1980), 283--292.

[85] Duffus, Dwight; Rival, Ivan A structure theory for ordered sets. Discrete Math. 35 (1981), 53--118.

[86] Duffus, D.; Rival, I.; Simonovits, M. Spanning retracts of a partially ordered set. Discrete Math. 32 (1980), no. 1, 1--7.

[87] Bisztriczky, Tibor; Rival, Ivan Continuous, slope-preserving maps of simple closed curves. Canad. J. Math. 32 (1980), no. 5, 1102--1113.

[88] Jónsson, Bjarni; Rival, Ivan Lattice varieties covering the smallest nonmodular variety. Pacific J. Math. 82 (1979), no. 2, 463--478.

[89] Rival, Ivan; Sands, Bill On the adjacency of vertices to the vertices of an infinite subgraph. J. London Math. Soc. (2) 21 (1980), no.3, 393--400.

[90] Duffus, Dwight; Poguntke, Werner; Rival, Ivan Retracts and the fixed point problem for finite partially ordered sets. Canad. Math. Bull. 23 (1980), no. 2, 231--236.

[91] Bollobás, Béla; Rival, Ivan The maximal size of the covering graph of a lattice. Algebra Universalis 9 (1979), no. 3, 371--373.

[92] Rival, Ivan; Sands, Bill Planar sublattices of a free lattice. II. Canad. J. Math. 31 (1979), no. 1, 17--34.

[93] Rival, Ivan; Sands, Bill Planar sublattices of a free lattice. I. Canad. J. Math. 30 (1978), no. 6, 1256-1283.

[94] Björner, Anders; Rival, Ivan A note on fixed points in semimodular lattices. Discrete Math. 29 (1980), no. 3, 245--250.

[95] Duffus, Dwight; Rival, Ivan A note on weak embeddings of distributive lattices. Algebra Universalis 10 (1980), no. 2, 258--259.

[96] Duffus, Dwight; Rival, Ivan Separable subsets of a finite lattice. J. Combin. Theory Ser. A 25 (1978), no. 2, 188--192.

[97] Rival, Ivan; Wille, Rudolf Lattices freely generated by partially ordered sets: which can be "drawn"? J. Reine Angew. Math. 310 (1979), 56-80.

[98] Duffus, Dwight; Rival, Ivan Retracts of partially ordered sets. J. Austral. Math. Soc. Ser. A 27 (1979), no. 4, 495--506.

[99] Nowakowski, Richard; Rival, Ivan Fixed-edge theorem for graphs with loops. J. Graph Theory 3 (1979), no. 4, 339--350.

[100] Nowakowski, Richard; Rival, Ivan Distributive cover-preserving sublattices of modular lattices. Nanta Math. 11 (1978), no. 2, 110--123.

[101] Rabinovitch, I.; Rival, I. The rank of a distributive lattice. Discrete Math. 25 (1979), no. 3, 275--279.

[102] Rival, Ivan; Sands, Bill A note on the congruence lattice of a finitely generated algebra. Proc. Amer. Math. Soc. 72 (1978), no.3, 451-455.

[103] Duffus, D.; Rival, I. Crowns in dismantlable partially ordered sets. Combinatorics (Proc. Fifth Hungarian Colloq., Keszthely, 1976), Vol. I, pp. 271--292, Colloq. Math. Soc. János Bolyai, 18, North-Holland, Amsterdam-New York, 1978.

[104] Duffus, Dwight; Rival, Ivan Path length in the covering graph of a lattice. Discrete Math. 19 (1977), no. 2, 139--158.

[105] Duffus, Dwight; Rival, Ivan A logarithmic property for exponents of partially ordered sets. Canad. J. Math. 30 (1978), no. 4, 797--807.

[106] Gaskill, Herbert S.; Rival, Ivan An exchange property for modular lattices. Algebra Universalis 8 (1978), no. 3, 354--356.

[107] Poguntke, W.; Rival, I. A theorem on finite sublattices of free lattices. Contributions to universal algebra (Colloq., József Attila Univ., Szeged, 1975), pp. 357--361. Colloq. Math. Soc. Janos Bolyai, Vol. 17, North-Holland, Amsterdam, 1977.

[108] Duffus, D.; Jónsson, B.; Rival, I. Structure results for function lattices. Canad. J. Math. 30 (1978), no. 2, 392--400.

[109] Davey, B. A.; Duffus, D.; Quackenbush, R. W.; Rival, I. Exponents of finite simple lattices. J. London Math. Soc. (2) 17 (1978), no. 2, 203--221.

[110] Nowakowski, Richard; Rival, Ivan The spectrum of a finite lattice: breadth and length techniques. Canad. Math. Bull. 20 (1977), no. 3, 319--329.

[111] Jónsson, Bjarni; Rival, Ivan Critical edges in subdirectly irreducible lattices. Proc. Amer. Math. Soc. 66 (1977), no. 2, 194--196.

[112] Rival, Ivan Combinatorial inequalities for semimodular lattices of breadth two. Algebra Universalis 6 (1976), no. 3, 303--311.

[113] Rival, Ivan A note on linear extensions of irreducible elements in a finite lattice. Algebra Universalis 6 (1976), no. 2, 99--103.

[114] Rival, Ivan A fixed point theorem for finite partially ordered sets. J. Combinatorial Theory Ser. A 21 (1976), no. 3, 309--318.

[115] Kelly, David; Rival, Ivan Crowns, fences, and dismantlable lattices. Canad. J. Math. 26 (1974), 1257--1271.

[116] Ganter, Bernhard; Rival, Ivan An arithmetical theorem for modular lattices. Algebra Universalis 5 (1975), no. 3, 395--396.

[117] Poguntke, Werner; Rival, Ivan Finite four-generated simple lattices contain all finite lattices. Proc. Amer. Math. Soc. 55 (1976), no. 1, 22--24.

[118] Davey, Brian A.; Rival, Ivan Finite sublattices of three-generated lattices. J. Austral. Math. Soc. Ser. A 21 (1976), no. 2, 171-178.

[119] Davey, B. A.; Poguntke, W.; Rival, I. A characterization of semi-distributivity. Algebra Universalis 5 (1975), 72--75.

[120] Rival, Ivan Sublattices of modular lattices of finite length. Canad. Math. Bull. 18 (1975), no. 1, 95--98.

[121] Kelly, David; Rival, Ivan Planar lattices. Canad. J. Math. 27 (1975), no. 3, 636--665.

[122] Rival, Ivan; Sands, Bill Weak embeddings and embeddings of finite distributive lattices. Arch. Math. (Basel) 26 (1975), no. 4, 346--352.

[123] Poguntke, Werner; Rival, Ivan Finite sublattices generated by order-isomorphic subsets. Arch. Math. (Basel) 25 (1974), 225--230.

[124] Rival, Ivan Maximal sublattices of finite distributive lattices. II. Proc. Amer. Math. Soc. 44 (1974), 263--268.

[125] Rival, Ivan Lattices with doubly irreducible elements. Canad. Math. Bull. 17 (1974), 91--95.

[126] Kelly, David; Rival, Ivan Certain partially ordered sets of dimension three. J. Combinatorial Theory Ser. A 18 (1975), 239--242.

[127] Antonius, Rachad; Rival, Ivan A note on Whitman's property for free lattices. Algebra Universalis 4 (1974), 271--272.

[128] Ganter, Bernhard; Rival, Ivan Dilworth's covering theorem for modular lattices: a simple proof. Algebra Universalis 3 (1973), 348--350.

[129] Rival, I. Projective images of modular (distributive, complemented) lattices are modular (distributive, complemented). Algebra Universalis 2 (1972), 395.

[130] Rival, Ivan Maximal sublattices of finite distributive lattices. Proc. Amer. Math. Soc. 37 (1973), 417--420.

[131] Hashemi, S. Mehdi; Kisielewicz, Andrzej; Rival, Ivan Upward drawings on planes and spheres (extended abstract). Graph drawing (Passau, 1995), 277--286, Lecture Notes in Comput. Sci., 1027, Springer, Berlin, 1996.

[132] Rival, Ivan Order, invariance and visibility. Words, languages and combinatorics (Kyoto, 1990), 444--453, World Sci. Publishing, River Edge, NJ, 1992.

[133] Rival, Ivan Dilworth's covering theorem for modular lattices. The Dilworth theorems, 261--264, Contemp. Mathematicians, Birkhäuser Boston, Boston, MA, 1990.

[134] Ewacha, Kevin; Rival, Ivan; Steiner, George Permutation schedules for flow shops with precedence constraints. Oper. Res. 38 (1990), no. 6, 1135--1139.

[135] Czyzowicz, Jurek; Rival, Ivan; Urrutia, Jorge Galleries, light matchings and visibility graphs. Algorithms and data structures (Ottawa, ON, 1989), 316--324, Lecture Notes in Comput. Sci., 382, Springer, Berlin, 1989.

[136] M. Alzohairi and I. Rival, 1996, Series-parallel Planar Ordered Sets have Pagenumber Two, GRAPH DRAWING '96, September 18 - 20, 1996, Berkeley, California

[137] G.-V. Jourdan, I. Rival and N. Zaguia. Upward Drawing on the Plane Grid Using Less Ink. Graph Drawing '94, Princeton, United States, October 1994.

[138] G.-V. Jourdan, I. Rival and N. Zaguia. Conjectures and Constructions About Perpendiculars Pairs—by Experiment. International Conference Formal Power Series and Algebraic Combinatorics '95, Marne-la-Vallée, France, June 1995.

[139] G.-V. Jourdan, I. Rival and N. Zaguia. Order Explorer, A System to See and Do in Four Dimensions. International Conference on Ordinal and Symbolic Data Analysis '95, Paris, France, June 1995.