相关论文: Asymptotic Behaviour of the Containment of Certain…

In this paper we consider the enumeration of ordered set partitions avoiding a permutation pattern of length 2 or 3. We provide an exact enumeration for avoiding the permutation 12. We also give exact enumeration for ordered partitions with…

We study Mallows random permutations conditioned to avoid a given pattern $\alpha$ of length~$3$. When the bias parameter is of the form $e^{\beta/n}$, we prove that these permutations converge to a non-trivial explicit deterministic…

We consider the enumeration of ordered set partitions avoiding a permutation pattern, as introduced by Godbole, Goyt, Herdan and Pudwell. Let $\op_{n,k}(p)$ be the number of ordered set partitions of $\{1,2,\ldots,n\}$ into $k$ blocks that…

In this work, we study the concept of self-overlapping permutations, which is related to the larger study of consecutive patterns in permutations. We show that this concept admits a simple and clear geometrical meaning, and prove that a…

Let $\pi_n$ be a uniformly chosen random permutation on $[n]$. Using an analysis of the probability that two overlapping consecutive $k$-permutations are order isomorphic, the authors of a recent paper showed that the expected number of…

Geometric grid classes of permutations have proven to be key in investigations of classical permutation pattern classes. By considering the representation of gridded permutations as words in a trace monoid, we prove that every geometric…

We introduce a new permutation statistic, namely, the number of cycles of length $q$ consisting of consecutive integers, and consider the distribution of this statistic among the permutations of $\{1,2,...,n\}$. We determine explicit…

We investigate the asymptotic behavior of posterior distributions of regression coefficients in high-dimensional linear models as the number of dimensions grows with the number of observations. We show that the posterior distribution…

Let $A$ be a set of natural numbers and let $S_{n,A}$ be the set of all permutations of $[n]=\{1,2,...,n\}$ with cycle lengths belonging to $A$. For $A(n)=A\cap [n]$, the limit $\rho=\lim_{n\to\infty}\mid A(n)\mid/n$ (if it esists) is…

An interesting feature of growth in animals is that different parts of the body grow at approximately the same rate. This property is called proportionate growth. In this paper, we review our recent work on patterns formed by adding $N$…

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…

A sequence of reversals that takes a signed permutation to the identity is perfect if at no step a common interval is broken. Determining a parsimonious perfect sequence of reversals that sorts a signed permutation is NP-hard. Here we show…

Consider a finite sequence of permutations of the elements 1,...,n, with the property that each element changes its position by at most 1 from any permutation to the next. We call such a sequence a tangle, and we define a move of element i…

Pattern formation often occurs in confined systems, yet how boundaries shape patterning dynamics is unclear. We develop techniques to analyze confinement effects in nonlocal advection-diffusion equations, which generically capture the…

An open conjecture in pattern avoidance theory is that the distribution of the major index among 321-avoiding permutations is distributed unimodally. We construct a formula for this distribution, and in the case of 2 descents prove…

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 goal of the paper is to study asymptotic behavior of the number of lost messages. Long messages are assumed to be divided into a random number of packets which are transmitted independently of one another. An error in transmission of a…

We consider a generalization of the Ewens measure for the symmetric group, calculating moments of the characteristic polynomial and similar multiplicative statistics. In addition, we study the asymptotic behavior of linear statistics (such…

In this paper, we study the occurrence of patterns in the cycle structures of permutations.

We develop the technique of reduced word manipulation to give a range of results concerning reduced words and permutations more generally. We prove a broad connection between pattern containment and reduced words, which specializes to our…