The Peak Statistics on Simsun Permutations

Ma, Shi-Mei; Yeh, Yeong‐Nan

doi:10.37236/5908

Cited by 9 publications

(7 citation statements)

References 17 publications

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“…Simsun permutations are useful in describing the action of the symmetric group on the maximal chains of the partition lattice (see [35,36]). There has been much recent work devoted to simsun permutation and its variations, see [11,24] and references therein.…”

Section: The G-index Of Young Tableauxmentioning

confidence: 99%

Derivatives, Eulerian polynomials and the $g$-indexes of Young tableaux

Han¹,

Ma²

2020

Preprint

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In this paper we first present summation formulas for k-order Eulerian polynomials and 1/k-Eulerian polynomials. We then present combinatorial expansions of (c(x)D) n in terms of inversion sequences as well as k-Young tableaux, where c(x) is a differentiable function in the indeterminate x and D is the derivative with respect to x. We define the g-indexes of k-Young tableaux and Young tableaux, which have important applications in combinatorics.By establishing some relations between k-Young tableaux and standard Young tableaux, we express Eulerian polynomials, second-order Eulerian polynomials, André polynomials and the generating polynomials of gamma coefficients of Eulerian polynomials in terms of standard Young tableaux, which imply a deep connection among these polynomials.

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Section: The G-index Of Young Tableauxmentioning

confidence: 99%

Derivatives, Eulerian polynomials and the $g$-indexes of Young tableaux

Han¹,

Ma²

2020

Preprint

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“…For example, (1,6,5,3,4)(2) is not a simsun permutation of the second kind since when we remove the letters 5 and 6, the resulting permutation (1,3,4)(2) contains the cycle double ascent 3. Let SS n be the set of the simsun permutations of the second kind of length n. It follows from [24,Eq. (18)] that…”

Section: Introductionmentioning

confidence: 99%

The gamma-positivity of Eulerian polynomials and succession statistics

Ma,

Yeh

et al. 2020

Preprint

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This paper is concerned with multivariate refinements of the γ-positivity of Eulerian polynomials by using the succession and fixed point statistics. Properties of the enumerative polynomials for permutations, signed permutations and derangements, including generating functions and γ-positivity are studied, which generalize and unify earlier results of Athanasiadis, Brenti, Chow, Petersen, Roselle, Stembridge, Shin and Zeng. In particular, we derive a formula expressing the joint distribution of excedance number and negative number statistics over the type B derangements in terms of the derangement polynomials.

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“…Simsun permutations are a variant of the André permutations of Foata and Schützenberger [9]. We refer the reader to [3,5,6,10,11] for some recent results related to simsun permutations.…”

Section: Introductionmentioning

confidence: 99%

“…There have been extensive studies of the descent polynomials for simsun permutations (see [5,11] for instance). Let S n (x) = π∈RSn x des A (π) , where des A (π) = |{i ∈ [n − 1] : π(i) > π(i + 1)}|.…”

Section: Introductionmentioning

confidence: 99%