Related papers: Monotone triangles and 312 Pattern Avoidance
We enumerate 132-avoiding permutations of order 3 in terms of the Catalan and Motzkin generating functions, answering a question of B\'{o}na and Smith from 2019. We also enumerate 231-avoiding permutations that are composed only of…
Alternating Sign Matrix(ASM for short) is a square matrix which is consist of 0, 1 and -1. In this paper, we characterize an ASM by showing a bijection between alternating sign matrix and six vertex model, and a bijection between six vertex…
The extension of pattern avoidance from ordinary permutations to those on multisets gave birth to several interesting enumerative results. We study permutations on regular multisets, i.e., multisets in which each element occurs the same…
A matching of the set $[2n]=\{ 1,2,\ldots ,2n\}$ is a partition of $[2n]$ into blocks with two elements, i.e. a graph on $[2n]$ such that every vertex has degree one. Given two matchings $\sigma$ and $\tau$ , we say that $\sigma$ is a…
We bound the number of permutations with a fixed number $r$ of $321 \ominus p_0$ patterns by a constant times the number of permutations which avoid $321 \ominus p_0$. We use this new upper bound to show that the ordinary generating…
A stronger version of an anomaly matching theorem (AMT) is proven that allows to anticipate the matching of continuous as well as discrete global anomalies. The AMT shows a connection between anomaly matching and the geometry of the null…
For each integer $n\ge 2$, we identify new infinite families of monogenic trinomials $f(x)=x^n+Ax^m+B$ with non-squarefree discriminant, many of which have small Galois group. These families are thus different from many previous…
We investigate multiplicative groups consisting entirely of singular alternating sign matrices (ASMs), and present several constructions of such groups. It is shown that every finite group is isomorphic to a group of singular ASMs, with a…
We enumerate the pattern class Av(2143,4231) and completely describe its permutations. The main tools are simple permutations and monotone grid classes.
Given permutations $\sigma \in S_k$ and $\pi \in S_n$ with $k<n$, the \emph{pattern matching} problem is to decide whether $\pi$ matches $\sigma$ as an order-isomorphic subsequence. We give a linear-time algorithm in case both $\pi$ and…
Following Anders and Archer, we say that an unordered rooted labeled forest avoids the pattern $\sigma\in\mathcal{S}_k$ if in each tree, each sequence of labels along the shortest path from the root to a vertex does not contain a…
We show how to enumerate words in $1^{m_1} \dots n^{m_n}$ that avoid the increasing consecutive pattern $12 \dots r$ for any $r \geq 2$. Our approach yields an $O(n^{s+1})$ algorithm to enumerate words in $1^s \dots n^s$, avoiding the…
By unifying various earlier extensions of alternating sign matrices (ASMs), we introduce the notion of prefix-bounded matrices (PBMs). It is shown that the convex hull of these matrices forms the intersection of two special generalized…
In this paper, we study pattern avoidance for stabilized-interval-free (SIF) permutations. These permutations are contained in the set of indecomposable permutations and in the set of derangements. We enumerate pattern-avoiding SIF…
This paper investigates pattern avoidance in linear extensions of a certain class of partially ordered set. Since the question of enumerating pattern avoiding linear extensions of posets in general is a very hard one, we focus instead on…
Let $S$ be a finite subset of ${\mathbb R}^2 \setminus (0,0)$. Generally, one would expect the pattern of lines $Ax + By = 1$, where $(A, B) \in S$ to contain polygons of all shapes and sizes. We show, however, that when $S$ is a…
Alternating sign matrices and totally symmetric self-complementary plane partitions are equinumerous sets of objects for which no explicit bijection is known. In this paper, we identify a subset of totally symmetric self-complementary plane…
The graph of overlapping permutations is defined in a way analogous to the De Bruijn graph on strings of symbols. That is, for every permutation $\pi = \pi_{1} \pi_{2} ... \pi_{n+1}$ there is a directed edge from the standardization of…
Given any polynomial system with fixed monomial term structure, we give explicit formulae for the generic number of roots with specified coordinate vanishing restrictions. For the case of affine space minus an arbitrary union of coordinate…
We investigate the intersection problem for finite semigroups, which asks for a given set of regular languages, represented by recognizing morphisms to finite semigroups, whether there exists a word contained in their intersection. We…