منابع مشابه
Plane posets, special posets, and permutations
We study the self-dual Hopf algebra HSP of special posets introduced by Malvenuto and Reutenauer and the Hopf algebra morphism from HSP to the Hopf algebra of free quasi-symmetric functions FQSym given by linear extensions. In particular, we construct two Hopf subalgebras both isomorphic to FQSym; the first one is based on plane posets, the second one on heap-ordered forests. An explicit isomor...
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We define a new object, called a signed poset, that bears the same relation to the hyperoctahedral group B n (i.e., signed permutations on n letters), as do posets to the symmetric group S n. We then prove hyperoctahedral analogues of the following results: (1) the generating function results from the theory of P-partitions; (2) the fundamental theorem of finite distributive lattices (or Birkho...
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We construct for each n an Eulerian partially ordered set Tn of rank n + 1 whose ce-index provides a non-commutative generalization of the n-th Tchebyshev polynomial. We show that the order complex of each Tn is shellable, homeomorphic to a sphere, and that its face numbers minimize the expression max|x|≤1 ∣∣∣∑nj=0(fj−1/fn−1) · 2−j · (x− 1)j∣∣∣ among the f -vectors of all (n − 1)-dimensional si...
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Baxter numbers are known to count several families of combinatorial objects, all of which come equipped with natural involutions. In this paper, we add a combinatorial family to the list, and show that the known bijections between these objects respect these involutions. We also give a formula for the number of objects fixed under this involution, showing that it is an instance of Stembridge’s ...
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In 1992 Drinfeld posed the question of finding the set-theoretic solutions of the Yang-Baxter equation. Recently, Gateva-Ivanova and Van den Bergh and Etingof, Schedler and Soloviev have shown a group-theoretical interpretation of involutive non-degenerate solutions. Namely, there is a oneto-one correspondence between involutive non-degenerate solutions on finite sets and groups of I-type. A gr...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2019
ISSN: 1077-8926
DOI: 10.37236/7273