Oriented Euler complexes and signed perfect matchings
نویسندگان
چکیده
منابع مشابه
Oriented Euler Complexes and Signed Perfect Matchings
This paper presents “oriented pivoting systems” as an abstract framework for complementary pivoting. It gives a unified simple proof that the endpoints of complementary pivoting paths have opposite sign. A special case are the Nash equilibria of a bimatrix game at the ends of Lemke–Howson paths, which have opposite index. For Euler complexes or “oiks”, an orientation is defined which extends th...
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We introduce a natural extension of Adin, Brenti, and Roichman’s major-index statistic nmaj on signed permutations (Adv. Appl. Math. 27, (2001), 210−244) to wreath products of a cyclic group with the symmetric group. We derive “insertion lemmas” which allow us to give simple bijective proofs that our extension has the same distribution as another statistic on wreath products introduced by Adin ...
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In the last decade there have been many results about special families of graphs whose number of perfect matchings is given by perfect or near perfect powers (N. Elkies et al., J. Algebraic Combin. 1 (1992), 111– 132; B.-Y. Yang, Ph.D. thesis, Department of Mathematics, MIT, Cambridge, MA, 1991; J. Propp, New Perspectives in Geometric Combinatorics, Cambridge University Press, 1999). In this pa...
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In 1961, P.W. Kasteleyn enumerated the domino tilings of a 2n × 2n chessboard. His answer was always a square or double a square (we call such a number "squarish"), but he did not provide a combinatorial explanation for this. In the present thesis, we prove by mostly combinatorial arguments that the number of matchings of a large class of graphs with 4-fold rotational symmetry is squarish; our ...
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We find recursive formulae for the number of perfect matchings in a graph G by splitting G into subgraphs H and Q. We use these formulas to count perfect matching of P hypercube Qn. We also apply our formulas to prove that the number of perfect matching in an edge-transitive graph is , where denotes the number of perfect matchings in G, is the graph constructed from by deleting edges with an en...
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ژورنال
عنوان ژورنال: Mathematical Programming
سال: 2014
ISSN: 0025-5610,1436-4646
DOI: 10.1007/s10107-014-0770-4