Combinatorics and Ordered Sets: Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference, Held August 11-17, 1985 ...For the mathematician interested in discrete mathematics, from the senior undergraduate to the professional level, this volume provides first-rate surveys of the important combinatorics themes in ordered sets. These expository lectures, given at a 1985 Joint Summer Research Conference, cover a wide range of topics, which include: the three-machine problem to illustrate the order-theoretic aspects of scheduling theory; the techniques used in settling the ``matching conjecture''; the decomposition of ordered sets into few chains; the reorientation of graphs; the varied occurrences of the meet-distribution property; surveys techniques used in settling binary sorting problems; the formulation of a general viewpoint for retraction; the survey of cutsets; and the role played by subdiagrams in ordered sets. |
Contents
Radon transforms in combinatorics and lattice theory | 33 |
Recursive ordered sets | 75 |
Orientations and reorientations of graphs | 103 |
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2-Helly property absolute retracts algebra algorithm alternating-cover antichain antichain cutset atomic binary combinatorial comparability graph conjecture construction contains convex correlated covering graph cutset property cycle defined denote Dilworth's directed graph distance distributive lattice edges element equivalent example exists expansion game Figure finite cutset finite ordered set fixed point geometric lattice graph G hyperconvex space incidence matrix infinite integer intersection involution isometric isomorphic J.Ginsburg L-player Lemma linear extension linear orderings m-machine problem m-machine schedule map f Math maximal antichain maximal chain meet-distributive metric spaces minimal Möbius function modular lattices morphism non-expansive mapping optimal order ideals orientations pair partially ordered sets polynomial posets Pouzet pr(A proof Proposition prove Radon transform rank reconstructed recursive chains recursive ordered set reflexive relations result retracts with respect Rival satisfying semigroup semigroup operation semimodular lattice sequence series-parallel structure subset Theorem theory vertices width winning strategy Zaguia