Related papers: Rectangulations avoiding a pattern
Transient growth due to non-normality is investigated for the Taylor-Couette problem with counter-rotating cylinders as a function of aspect ratio eta and Reynolds number Re. For all Re < 500, transient growth is enhanced by curvature, i.e.…
Shallow permutations were defined in 1977 to be those that satisfy the lower bound of the Diaconis-Graham inequality. Recently, there has been renewed interest in these permutations. In particular, Berman and Tenner showed they satisfy…
In the present note, we examine the behavior of some homo\-thecy-invariant differentiation basis of rectangles in the plane satisfying the following requirement: for a given rectangle to belong to the basis, the ratio of the largest of its…
(Work in progress) Marcus and Tardos \cite{MarcusTardos2004} proved the Stanley--Wilf conjecture by reducing pattern avoidance to an extremal problem on $0$--$1$ matrices. We give a parallel proof for classical permutation patterns that…
Partially ordered patterns (POPs) play an important role in the study of permutation patterns, providing a convenient framework for describing large families of classical patterns. The problem of enumerating permutations that avoid POPs has…
Permutons are probability measures on the unit square with uniform marginals that provide a natural way to describe limits of permutations. We are interested in the permuton limits for permutations sampled uniformly from certain…
In this paper, we find an explicit formula for the generating function that counts the circular permutations of length n avoiding the pattern 23 4 1 whose enumeration was raised as an open problem by Rupert Li. This then completes in all…
We consider long-range percolation on $\mathbb{Z}^d$, where the probability that two vertices at distance $r$ are connected by an edge is given by $p(r)=1-\exp[-\lambda(r)]\in(0,1)$ and the presence or absence of different edges are…
Rectangulations are partitions of a square into axis-aligned rectangles. A number of results provide bijections between combinatorial equivalence classes of rectangulations and families of pattern-avoiding permutations. Other results deal…
We investigate pattern avoidance in alternating permutations and generalizations thereof. First, we study pattern avoidance in an alternating analogue of Young diagrams. In particular, we extend Babson-West's notion of shape-Wilf…
We extend the concept of pattern avoidance in permutations on a totally ordered set to pattern avoidance in permutations on partially ordered sets. The number of permutations on $P$ that avoid the pattern $\pi$ is denoted $Av_P(\pi)$. We…
We investigate a lattice model of comb polymers and derive bounds on the exponential growth rate of the number of embeddings of the comb. A comb is composed of a backbone that is a self-avoiding walk and a set of $t$ teeth, also modelled as…
Since the control of the Lipschitz constant has a great impact on the training stability, generalization, and robustness of neural networks, the estimation of this value is nowadays a real scientific challenge. In this paper we introduce a…
For a bilinear map $*:\mathbb R^d\times \mathbb R^d\to \mathbb R^d$ of nonnegative coefficients and a vector $s\in \mathbb R^d$ of positive entries, among an exponentially number of ways combining $n$ instances of $s$ using $n-1$…
Pattern-avoiding permutations are a central object of study in both combinatorics and theoretical computer science. In this paper we design a data structure that can store any size-$n$ permutation $\tau$ that avoids an arbitrary (and…
In this paper, we consider pattern avoidance in a subset of words on $\{1,1,2,2,\dots,n,n\}$ called reverse double lists. In particular a reverse double list is a word formed by concatenating a permutation with its reversal. We enumerate…
Sergey Kitaev has shown that the exponential generating function for permutations avoiding the generalized pattern $\sigma$-$k$, where $\sigma$ is a pattern without dashes and $k$ is one greater than the biggest element in $\sigma$, is…
We characterize the formulas that are avoided by every $\alpha$-free word for some $\alpha>1$. We study the avoidability index of formulas whose fragments are of the form $XYX$. The largest avoidability index of an avoidable palindrome…
One of the least studied universal deformations of incompressible nonlinear elasticity, namely the straightening of a sector of a circular cylinder into a rectangular block, is revisited here and, in particular, issues of existence and…
The exponential growth rate of non polynomially growing subgroups of $GL_d$ is conjectured to admit a uniform lower bound. This is known for non-amenable subgroups, while for amenable subgroups it is known to imply the Lehmer conjecture…