A refined sign-balance of simsun permutations

Eu, Sen-Peng; Fu, Tung-Shan; Pan, Yeh-Jong

doi:10.1016/j.ejc.2013.05.001

Cited by 8 publications

(6 citation statements)

References 16 publications

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“…In addition to T (0, 2, 1) and T (1, 2, 1), the polynomials defined on T (1, 2, 3) also correspond, by (50), to second-order Eulerian numbers, and appeared in [88], together with two other variants:…”

Section: And [29]mentioning

confidence: 99%

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An asymptotic distribution theory for Eulerian recurrences with applications

Hwang

Chern

Duh

2020

Advances in Applied Mathematics

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We study linear recurrences of Eulerian type of the formwith P 0 (v) given, where α(v), β(v) and γ(v) are in most cases polynomials of low degrees. We characterize the various limit laws of the coefficients of P n (v) for large n using the method of moments and analytic combinatorial tools under varying α(v), β(v) and γ(v), and apply our results to more than two hundred of concrete examples when β(v) = 0 and more than three hundred when β(v) = 0 that we collected from the literature and from Sloane's OEIS database. The limit laws and the convergence rates we worked out are almost all new and include normal, half-normal, Rayleigh, beta, Poisson, negative binomial, Mittag-Leffler, Bernoulli, etc., showing the surprising richness and diversity of such a simple framework, as well as the power of the approaches used.

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Section: And [29]mentioning

confidence: 99%

“…Then (88) follows from noticing that the m-th moment of a Beta(a, b) random variable is given by Γ(a + b)Γ(m + a) Γ(a)Γ(m + a + b) (a, b, 0; m = 0, 1, . .…”

Section: Beta Limit Laws and Their Mixtures ( β α = −1)mentioning

confidence: 99%

An asymptotic distribution theory for Eulerian recurrences with applications

Hwang

Chern

Duh

2020

Advances in Applied Mathematics

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“…• From symmetric group to other reflection groups by Reiner [27], Adin-Gessel-Roichman [1], Biagioli [6], Biagioli-Caselli [8] and Chang-Eu-Fu-Lin-Lo [12], to name a few. • To restricted permutations such as 321-avoiding permutations by Adin-Roichman [3] and Eu-Fu-Pan-Ting [15], Simsun permutations by Eu-Fu-Pan [14], PRW permutations by Lin-Wang-Zeng [22] and permutations with subsequence restrictions by Eu-Fu-Hsu-Liao-Sun [16].…”

Section: Introductionmentioning

confidence: 99%

Signed Euler-Mahonian identities

Eu¹,

Zhao²,

Lo³

2020

Preprint

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A relationship between signed Eulerian polynomials and the classical Eulerian polynomials on Sn was given by Désarménien and Foata in 1992, and a refined version, called signed Euler-Mahonian identity, together with a bijective proof were proposed by Wachs in the same year. By generalizing this bijection, in this paper we extend the above results to the Coxeter groups of types Bn, Dn, and the complex reflection group G(r, 1, n), where the 'sign' is taken to be any one-dimensional character. Some obtained identities can be further restricted on some particular set of permutations. We also derive some new interesting sign-balance polynomials for types Bn and Dn.

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“…They are a variant of André permutations that was introduced by Foata and Schützenberge [12]. There has been much recent work related to simsun permutations (see [3,5,8,11,13,15] for instance).…”

Section: Introductionmentioning

confidence: 99%