Related papers: On some properties of permutation tableaux

In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…

We compute the number of ways a given permutation can be written as a product of exactly $k$ transpositions. We express this number as a linear combination of explicit geometric sequences, with coefficients which can be computed in many…

Random-matrix theory is applied to transition-rate matrices in the Pauli master equation. We study the distribution and correlations of eigenvalues, which govern the dynamics of complex stochastic systems. Both the cases of identical and of…

A celebrated analogy between prime factorizations of integers and cycle decompositions of permutations is explored here. Asymptotic formulas characterizing semismooth numbers (possessing at most several large factors) carry over to random…

We consider the distribution of cycles in two models of random permutations, that are related to one another. In the first model, cycles receive a weight that depends on their length. The second model deals with permutations of points in…

The class of bipartite permutation graphs enjoys many nice and important properties. In particular, this class is critically important in the study of clique- and rank-width of graphs, because it is one of the minimal hereditary classes of…

In this paper, we study the generating functions for the number of pattern restricted Stirling permutations with a given number of plateaus, descents and ascents. Properties of the generating functions, including symmetric properties and…

This is a presentation of recent work on quantum permutation groups, complex Hadamard matrices, and the connections between them. A long list of problems is included. We include as well some conjectural statements, about matrix models.

In this paper, we focus on the enumeration of permutations by number of cyclic occurrence of peaks and valleys. We find several recurrence relations involving the number of permutations with a prescribed number of cyclic peaks, cyclic…

We present some results on the proportion of permutations of length $n$ containing certain mesh patterns as $n$ grows large, and give exact enumeration results in some cases. In particular, we focus on mesh patterns where entire rows and…

The interval poset of a permutation catalogues the intervals that appear in its one-line notation, according to set inclusion. We study this poset, describing its structural, characterizing, and enumerative properties.

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 article, we study a non-uniform distribution on permutations biased by their number of records that we call \emph{record-biased permutations}. We give several generative processes for record-biased permutations, explaining also how…

The extremal characteristics of random structures, including trees, graphs, and networks, are discussed. A statistical physics approach is employed in which extremal properties are obtained through suitably defined rate equations. A variety…

We introduce the mathematical theory of the particle systems that interact via permutations, where the transition rates are assigned not to the jumps from a site to a site, but to the permutations themselves. This permutation processes can…

Starting from some considerations we make about the relations between certain difference statistics and the classical permutation statistics we study permutations whose inversion number and excedance difference coincide. It turns out that…

We discuss both simple and more subtle connections between the numbers of permutations and full cycles with some restrictions,in particular, between the numbers of permutations and full cycles with prescribed up-down structure.

We look at geometric limits of large random non-uniform permutations. We mainly consider two theories for limits of permutations: permuton limits, introduced by Hoppen, Kohayakawa, Moreira, Rath, and Sampaio to define a notion of scaling…

The aim of this paper is to describe a population model with transition. We analyze the spectral properties of the transition matrix considering both irreducible and reducible structures. We give physical interpretations of these properties…

In this paper we investigate a permutation statistic that was independently introduced by Romik in 2005. This statistic counts the number of bumps that occur during the execution of the Robinson-Schensted procedure when applied to a given…