منابع مشابه
Eulerian Quasisymmetric Functions
We introduce a family of quasisymmetric functions called Eulerian quasisymmetric functions, which specialize to enumerators for the joint distribution of the permutation statistics, major index and excedance number on permutations of fixed cycle type. This family is analogous to a family of quasisymmetric functions that Gessel and Reutenauer used to study the joint distribution of major index a...
متن کاملUnimodality of Eulerian quasisymmetric functions
We prove two conjectures of Shareshian and Wachs about Eulerian quasisymmetric functions and polynomials. The first states that the cycle type Eulerian quasisymmetric function Qλ,j is Schur-positive, and moreover that the sequence Qλ,j as j varies is Schur-unimodal. The second conjecture, which we prove using the first, states that the cycle type (q, p)-Eulerian polynomial A λ (q, p, q −1t) is ...
متن کاملEulerian Quasisymmetric Functions and Cyclic Sieving
Abstract. It is shown that a refined version of a q-analogue of the Eulerian numbers together with the action, by conjugation, of the subgroup of the symmetric group Sn generated by the ncycle (1, 2, . . . , n) on the set of permutations of fixed cycle type and fixed number of excedances provides an instance of the cyclic sieving phenonmenon of Reiner, Stanton and White. The main tool is a clas...
متن کاملPeak Quasisymmetric Functions and Eulerian Enumeration
Via duality of Hopf algebras, there is a direct association between peak quasisymmetric functions and enumeration of chains in Eulerian posets. We study this association explicitly, showing that the notion of cd-index, long studied in the context of convex polytopes and Eulerian posets, arises as the dual basis to a natural basis of peak quasisymmetric functions introduced by Stembridge. Thus E...
متن کاملEulerian Quasisymmetric Functions and Poset Topology
We introduce a family of quasisymmetric functions called Eulerian quasisymmetric functions, which have the property of specializing to enumerators for the joint distribution of the permutation statistics, major index and excedance number on permutations of fixed cycle type. This family is analogous to a family of quasisymmetric functions that Gessel and Reutenauer used to study the joint distri...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2010
ISSN: 0001-8708
DOI: 10.1016/j.aim.2010.05.009