Related papers: Permutation Tableaux and the Dashed Permutation Pa…
We extend work of McKay, Morse, and Wilf by giving exact formulas and asymptotic formulas for the number of skew Young tableaux T in two situations: (1) the "inside shape" and total number of cells of T are fixed, and (2) the inside shape…
We present a simple a bijection between permutations of $\{1,..., n\}$ with $k$ descents and permutation tableaux of length $n$ with $k$ columns.
In 1953, Carlitz~\cite{Car53} showed that all permutation polynomials over $\F_q$, where $q>2$ is a power of a prime, are generated by the special permutation polynomials $x^{q-2}$ (the inversion) and $ ax+b$ (affine functions, where $0\neq…
We consider a recursive record-filtering procedure, which we informally call Disappear-Sort. Let $D_n$ denote the random variable giving the required number of passes in Disappear-Sort to eliminate a sequence of length $n$ sampled as i.i.d.…
Let $D$ be an oriented graph. The inversion of a set $X$ of vertices in $D$ consists in reversing the direction of all arcs with both ends in $X$. The inversion number of $D$, denoted by ${\rm inv}(D)$, is the minimum number of inversions…
In the last years, different types of patterns in permutations have been studied: vincular, bivincular and mesh patterns, just to name a few. Every type of permutation pattern naturally defines a corresponding computational problem: Given a…
We present a simplified variant of Biane's bijection between permutations and 3-colored Motzkin paths with weight that keeps track of the inversion number, excedance number and a statistic so-called depth of a permutation. This generalizes…
We show that many infinite classes of permutations over finite fields can be constructed via translators with a large choice of parameters. We first charac- terize some functions having linear translators, based on which several families of…
A permutation is called {\it {block-wise simple}} if it contains no interval of the form $p_1\oplus p_2$ or $p_1 \ominus p_2$. We present this new set of permutations and explore some of its combinatorial properties. We present a generating…
The diagram of a 132-avoiding permutation can easily be characterized: it is simply the diagram of a partition. Based on this fact, we present a new bijection between 132-avoiding and 321-avoiding permutations. We will show that this…
Inspired by a width invariant on permutations defined by Guillemot and Marx, Bonnet, Kim, Thomass\'e, and Watrigant introduced the twin-width of graphs, which is a parameter describing its structural complexity. This invariant has been…
We study a modification of Kendall's tau-test, replacing his permutations of n different numbers by sequences of length n, where repetition is allowed. In particular, binary sequences are included. Random sequences can be tested.
We use the 0-1 tableaux as a tool for enumerating permutations and partitions with restricted minima. The method used is extended for permutation pairs and partition pairs generated by a bipartite 0-1 tableaux.
In this paper, we consider the problem of reconstructing an $n \times n$ cell matrix $D(\vec{x})$ constructed from a vector $\vec{x} = (x_{1}, x_{2},\dots, x_{n})$ of positive real numbers, from a given set of spectral data. In addition, we…
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…
We show that for any permutation $\pi$ there exists an integer $k_{\pi}$ such that every permutation avoiding $\pi$ as a pattern is a product of at most $k_{\pi}$ separable permutations. In other words, every strict class $\mathcal C$ of…
The {\it inversion} of a set $X$ of vertices in a digraph $D$ consists in reversing the direction of all arcs of $D\langle X\rangle$. The {\it inversion number} of an oriented graph $D$, denoted by ${\rm inv}(D)$, is the minimum number of…
In this paper we study alternative tableaux introduced by Viennot. These tableaux are in simple bijection with permutation tableaux, defined previously by Postnikov . We exhibit a simple recursive structure for alternative tableaux. From…
The NP-complete Permutation Pattern Matching problem asks whether a $k$-permutation $P$ is contained in a $n$-permutation $T$ as a pattern. This is the case if there exists an order-preserving embedding of $P$ into $T$. In this paper, we…
We prove that the generating function for the number of flattened permutations having a given number of occurrences of the pattern 13-2 is rational, by using the recurrence relations and the kernel method.