Related papers: Linked Partitions and Permutation Tableaux

Using the bijection between partitions and vacillating tableaux, we establish a correspondence between pairs of noncrossing free Dyck paths of length $2n$ and noncrossing partitions of $[2n+1]$ with $n+1$ blocks. In terms of the number of…

We write $S_{\leq n}(A)$ and $\Part_{\fin}(A)$ for the set of permutations with at most $n$ non-fixed points, where $n$ is a natural number, and the set of partitions whose members are finite, respectively, of a set $A$. Among our results,…

We consider the relation between various permutation statistics and properties of permutation tableaux. We answer some of the questions of Steingrimsson and Williams (math.CO/0507149), in particular, on the distribution of the bistatistic…

The Interval poset of a permutation is an effective way of capturing all the intervals of the permutation and the inclusions between them and was introduced recently by Tenner. Thi paper explores the geometric interpretation of interval…

The lattice of partitions of a set and its d-divisible generalization have been much studied for their combinatorial, topological, and representation-theoretic properties. An ordered set partition is a set partition where the subsets are…

In 2000 Babson and Steingr{\'\i}msson introduced the notion of vincular patterns in permutations. They shown that essentially all well-known Mahonian permutation statistics can be written as combinations of such patterns. Also, they proved…

We present a bijection between cyclic permutations of {1,2,...,n+1} and permutations of {1,2,...,n} that preserves the descent set of the first n entries and the set of weak excedances. This non-trivial bijection involves a Foata-like…

The pattern-avoiding fillings of Young diagrams we study arose from Postnikov's work on positive Grassman cells. They are called Le-diagrams, and are in bijection with decorated permutations. Other closely-related diagrams are interpreted…

In this paper we present an extension of Stanley's theorem related to partitions of positive integers. Stanley's theorem states a relation between "the sum of the numbers of distinct members in the partitions of a positive integer $n$" and…

We present a bijection between non-crossing partitions of the set $[2n+1]$ into $n+1$ blocks such that no block contains two consecutive integers, and the set of sequences $\{s_{i}\}_{1}^{n}$ such that $1 \leq s_{i} \leq i$, and if…

Permutation-partition pairs were introduced by Stahl in 1980. These pairs are generalizations of graphs and graphs on surfaces. They were used to solve some problems for orientable embeddings of graphs. In this paper, we introduce a…

In this paper, we introduce a class of $(P, \omega)$-partitions that we call periodic $(P, \omega)$-partitions, then prove that such $(P, \omega)$-partitions satisfy a homogeneous first-order matrix difference equation. After defining an…

This paper establishes an analogue of the Robinson--Schensted correspondence for cylindric tableaux. In particular, for any pair of positive integers $(d,L)$, we construct a bijection between permutations that avoid the patterns $d\cdots 1…

In this note a bijection is constructed between the set of partitions of n simultaneously s-regular and t-distinct, and those simultaneously t-regular and s-distinct. Some implications of the map are discussed. As a generalized version of…

In this paper we consider permutations of sequences of partitions, obtaining a result which parallels von Neumann's theorem on permutations of dense sequences and uniformly distributed sequences of points.

An involution in a Coxeter group has an associated set of involution words, a variation on reduced words. These words are saturated chains in a partial order first considered by Richardson and Springer in their study of symmetric varieties.…

We present a bijective algorithm with which an arbitrary permutation decomposes canonically into elementary blocks which we call families, which are sets with a specified number of ascents and descents. We show that families, arranged in an…

Let $L(m,n)$ denote Young's lattice, consisting of all partitions whose Young diagrams are contained within an $m\times n$ rectangle. It is a classical result that the partially ordered set $L(m,n)$ is rank-symmetric, rank-unimodal, and…

Recently, Blecher and Knopfmacher applied the notion of fixed points to integer partitions. This has already been generalized and refined in various ways such as $h$-fixed points for an integer parameter $h$ by Hopkins and Sellers. Here, we…

A set partition of $[n] := \{1, 2, \dots, n \}$ is called {\em $r$-Stirling} if the numbers $1, 2, \dots, r$ belong to distinct blocks. Haglund, Rhoades, and Shimozono constructed graded ring $R_{n,k}$ depending on two positive integers $k…