相关论文: The equidistribution of some Mahonian statistics o…
Babson and Steingr\'{\i}msson introduced generalized permutation patterns and showed that most of the Mahonian statistics in the literature can be expressed by the combination of generalized pattern functions. Particularly, they defined a…
The study of Mahonian statistics dated back to 1915 when MacMahon showed that the major index and the inverse number have the same distribution on a set of permutations with length n. Since then, many Mahonian statistics have been…
A Mahonian d-function is a Mahonian statistic that can be expressed as a linear combination of vincular pattern statistics of length at most d. Babson and Steingrimsson classified all Mahonian 3-functions up to trivial bijections and…
We give a direct combinatorial proof of the equidistribution of two pairs of permutation statistics, (des, aid) and (lec, inv), which have been previously shown to have the same joint distribution as (exc, maj), the major index and the…
Babson and Steingr\'{\i}msson introduced generalized permutation patterns and showed that most of the Mahonian statistics in the literature can be expressed by the combination of generalized pattern functions. Particularly, they defined a…
In 2000, Babson and Steingr\'{i}msson generalized the notion of permutation patterns to the so-called vincular patterns, and they showed that many Mahonian statistics can be expressed as sums of vincular pattern occurrence statistics. STAT…
Our first main result shows that, for words with a fixed multiset of weak right-to-left minima, the statistics within each of the following three classes are equidistributed: 1. Mahonian statistics: $\textsf{inv}$, $\textsf{maj}$,…
We prove that the pair of statistics (des,maj) on multiset permutations is equidistributed with the pair (stc,inv) on certain quotients of the symmetric group. We define the analogue of the statistic stc on multiset permutations, whose…
The distribution of certain Mahonian statistic (called $\mathrm{BAST}$) introduced by Babson and Steingr\'{i}msson over the set of permutations that avoid vincular pattern $1\underline{32}$, is shown bijectively to match the distribution of…
Finding distributions of permutation statistics over pattern-avoiding classes of permutations attracted much attention in the literature. In particular, Bukata et al. found distributions of ascents and descents on permutations avoiding any…
Br\"and\'en and Claesson introduced mesh patterns to provide explicit expansions for certain permutation statistics as linear combinations of (classical) permutation patterns. The first systematic study of avoidance of mesh patterns was…
Two well-known distributions in the study of permutation statistics are the Mahonian and Eulerian distributions. Mahonian statistics include the major index MAJ and the number of inversions INV, while examples of Eulerian statistics are the…
The inversion number and the major index are equidistributed on the symmetric group. This is a classical result, first proved by MacMahon, then by Foata by means of a combinatorial bijection. Ever since many refinements have been derived,…
We study the distribution of the statistics 'number of fixed points' and 'number of excedances' in permutations avoiding subsets of patterns of length 3. We solve all the cases of simultaneous avoidance of more than one pattern, giving…
Recently, Babson and Steingrimsson (see \cite{BS}) introduced generalized permutations patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. Following \cite{BCS}, let $e_k\pi$…
The standard algorithm for generating a random permutation gives rise to an obvious permutation statistic $\stat$ that is readily seen to be Mahonian. We give evidence showing that it is not equal to any previously published statistic. Nor…
A systematic study of avoidance of mesh patterns of length 2 was conducted by Hilmarsson et al., where 25 out of 65 non-equivalent cases were solved. In this paper, we give 27 distribution results for these patterns including 14…
Dokos et. al. studied the distribution of two statistics over permutations $\mathfrak{S}_n$ of $\{1,2,\dots, n\}$ that avoid one or more length three patterns. A permutation $\sigma\in\mathfrak{S}_n$ contains a pattern…
In a recent paper, Goyt and Sagan studied distributions of certain set partition statistics over pattern restricted sets of set partitions that were counted by the Fibonacci numbers. Their study produced a class of $q$-Fibonacci numbers,…
We prove that the Mahonian-Stirling pairs of permutation statistics $(\sor, \cyc)$ and $(\inv, \mathrm{rlmin})$ are equidistributed on the set of permutations that correspond to arrangements of $n$ non-atacking rooks on a Ferrers board with…