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Answering a question of Clark and Ehrenborg (2010), we determine asymptotics for the number of permutations of size n that admit the most common excedance set. In fact, we provide a more general bivariate asymptotic using the multivariate asymptotic methods of R. Pemantle and M. C. Wilson. We also consider two applications of our main result. First, we determine asymptotics on the number of permutations of size n which simultaneously avoid the generalized patterns 21-34 and 34-21. Second, we determine asymptotics on the number of n-cycles that admit no stretching pairs.
We consider properties of the box polynomials, a one variable polynomial defined over all integer partitions $lambda$ whose Young diagrams fit in an $m$ by $n$ box. We show that these polynomials can be expressed by the finite difference operator app
A formula of Stembridge states that the permutation peak polynomials and descent polynomials are connected via a quadratique transformation. The aim of this paper is to establish the cycle analogue of Stembridges formula by using cycle peaks and exce
The object of this paper is to give a systematic treatment of excedance-type polynomials. We first give a sufficient condition for a sequence of polynomials to have alternatingly increasing property, and then we present a systematic study of the join
Recently, Bagno, Garber and Mansour studied a kind of excedance number on the complex reflection groups and computed its multidistribution with the number of fixed points on the set of involutions in these groups. In this note, we consider the simila
In 1973, Brown, ErdH{o}s and Sos proved that if $mathcal{H}$ is a 3-uniform hypergraph on $n$ vertices which contains no triangulation of the sphere, then $mathcal{H}$ has at most $O(n^{5/2})$ edges, and this bound is the best possible up to a consta