Related papers: Reduced word manipulation: patterns and enumeratio…
We give an algorithmic-bijective proof of Macdonald's reduced word identity in the theory of Schubert polynomials, in the special case where the permutation is dominant. Our bijection uses a novel application of David Little's generalized…
Words in natural language follow a Zipfian distribution whereby some words are frequent but most are rare. Learning representations for words in the "long tail" of this distribution requires enormous amounts of data. Representations of rare…
We use the cluster method to enumerate permutations avoiding consecutive patterns. We reprove and generalize in a unified way several known results and obtain new ones, including some patterns of length 4 and 5, as well as some infinite…
Words in some natural languages can have a composite structure. Elements of this structure include the root (that could also be composite), prefixes and suffixes with which various nuances and relations to other words can be expressed.…
Recent methods for learning vector space representations of words have succeeded in capturing fine-grained semantic and syntactic regularities using vector arithmetic. However, these vector space representations (created through large-scale…
Catalan words are particular growth-restricted words counted by the eponymous integer sequence. In this article we consider Catalan words avoiding a pair of patterns of length 3, pursuing the recent initiating work of the first and last…
We develop a new, powerful method for counting elements in a multiset. As a first application, we use this algorithm to study the number of occurrences of patterns in a permutation. For patterns of length 3 there are two Wilf classes, and…
Learning word embeddings using distributional information is a task that has been studied by many researchers, and a lot of studies are reported in the literature. On the contrary, less studies were done for the case of multiple languages.…
How can we compress language models without sacrificing accuracy? The number of compression algorithms for language models is rapidly growing to benefit from remarkable advances of recent language models without side effects due to the…
Given a permutation w, we look at the range of how often a simple reflection s_k appears in reduced decompositions of w. We compute the minimum and give a sharp upper bound on the maximum. That bound is in terms of 321- and 3412-patterns in…
In this paper, we explore applications of combinatorics on words across various domains, including data compression, error detection, cryptographic protocols, and pseudorandom number generation. The examination of the theoretical…
We present a model of speech perception which takes into account effects of correlations between sounds. Words in this model correspond to the attractors of a suitably chosen descent dynamics. The resulting lexicon is rich in short words,…
We consider avoidance of permutation patterns with designated gap sizes between pairs of consecutive letters. We call the patterns having such constraints distant patterns (DPs) and we show their relation to other pattern notions…
Permutations are usually enumerated by size, but new results can be found by enumerating them by inversions instead, in which case one must restrict one's attention to indecomposable permutations. In the style of the seminal paper by Simion…
Following a question of J. Cooper, we study the expected number of occurrences of a given permutation pattern $q$ in permutations that avoid another given pattern $r$. In some cases, we find the pattern that occurs least often, (resp. most…
In this thesis, we consider the problem of characterizing and enumerating sets of polyominoes described in terms of some constraints, defined either by convexity or by pattern containment. We are interested in a well known subclass of…
We investigate a generalization of stacks that we call $\mathcal{C}$-machines. We show how this viewpoint rapidly leads to functional equations for the classes of permutations that $\mathcal{C}$-machines generate, and how these systems of…
An infinite permutation is a linear ordering of the set of non-negative integers. Generally, the properties of infinite permutations analogous to those of infinite words show some resemblances and some differences between permutations and…
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…
Using techniques from Poisson approximation, we prove explicit error bounds on the number of permutations that avoid any pattern. Most generally, we bound the total variation distance between the joint distribution of pattern occurrences…