Related papers: A note on the avoidability of binary patterns with…
Patterns are words with terminals and variables. The language of a pattern is the set of words obtained by uniformly substituting all variables with words that contain only terminals. In their original definition, patterns only allow for…
As suggested by Currie, we apply the probabilistic method to problems regarding pattern avoidance. Using techniques from analytic combinatorics, we calculate asymptotic pattern occurrence statistics and use them in conjunction with the…
We present a family of avoidable formulas with reversal whose avoidability index is unbounded. We also complete the determination of the avoidability index of the formulas with reversal in the 3-avoidance basis.
Patterns are words with terminals and variables. The language of a pattern is the set of words obtained by uniformly substituting all variables with words that contain only terminals. Regular constraints restrict valid substitutions of…
Moir\'e patterns are omnipresent. They are important for any overlapping periodic phenomenon, from vibrational and electromagnetic, to condensed matter. Here we show, both theoretically and via experimental simulations by ultracold atoms,…
In this paper, we study the pattern occurrence in $k$-ary words. We prove an explicit upper bound on the number of $k$-ary words avoiding any given pattern using a random walk argument. Additionally, we reproduce several already known…
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…
It is "well known" that in linear models: (1) testable constraints on the marginal distribution of observed variables distinguish certain cases in which an unobserved cause jointly influences several observed variables; (2) the technique of…
Recently, Babson and Steingrimsson have introduced generalised permutation patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. We consider pattern avoidance for such patterns, and…
We examine the modular properties of nonrenormalizable superpotential terms in string theory and show that the requirement of modular invariance necessitates the nonvanishing of certain Nth order nonrenormalizable terms. In a class of…
We enumerate and characterize some classes of alternating and reverse alternating involutions avoiding a single pattern of length three or four. If on one hand the case of patterns of length three is trivial, on the other hand, the length…
Why do some languages like Czech permit free word order, while others like English do not? We address this question by pretraining transformer language models on a spectrum of synthetic word-order variants of natural languages. We observe…
The scope of this paper is two-fold. First, to present to the researchers in combinatorics an interesting implementation of permutations avoiding generalized patterns in the framework of discrete-time dynamical systems. Indeed, the orbits…
An occurrence of a classical pattern p in a permutation \pi is a subsequence of \pi whose letters are in the same relative order (of size) as those in p. In an occurrence of a generalized pattern, some letters of that subsequence may be…
We find finite-state recurrences to enumerate the words on the alphabet $[n]^r$ which avoid the patterns 123 and $1k(k-1)\dots2$, and, separately, the words which avoid the patterns 1234 and $1k(k-1)\dots2$.
Causal discovery from data affected by unobserved variables is an important but difficult problem to solve. The effects that unobserved variables have on the relationships between observed variables are more complex in nonlinear cases than…
This paper begins with a comprehensive overview of combinatorics on words and symbolic dynamics, covering their historical origins, fundamental concepts, and interconnections. Building upon this foundation, we introduce novel mathematical…
We characterize the squares occurring in infinite overlap-free binary words and construct various alpha power-free binary words containing infinitely many overlaps.
The periodic (ordinal) patterns of a map are the permutations realized by the relative order of the points in its periodic orbits. We give a combinatorial characterization of the periodic patterns of an arbitrary signed shift, in terms of…
We study regular expressions that use variables, or parameters, which are interpreted as alphabet letters. We consider two classes of languages denoted by such expressions: under the possibility semantics, a word belongs to the language if…