Related papers: Words restricted by 3-letter generalized multiperm…
Extended regular expressions with counting and interleaving are widely used in practice. However the related theoretical studies for this kind of expressions currently cannot meet the need of practical work. This paper develops syntax…
We construct an infinite word $w$ over the $5$-letter alphabet such that for every factor $f$ of $w$ of length at least two, there exists a cyclic permutation of $f$ that is not a factor of $w$. In other words, $w$ does not contain a…
In this paper, we compute the distributions of the statistic number of crossings over permutations avoiding one of the pairs $\{321,231\}$, $\{123,132\}$ and $\{123,213\}$. The obtained results are new combinatorial interpretations of two…
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…
We investigate the number of sets of words that can be formed from a finite alphabet, counted by the total length of the words in the set. An explicit expression for the counting sequence is derived from the generating function, and…
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…
We present a method for the enumeration of restricted words over a finite alphabet. Restrictions are described through the inclusion or exclusion of suitable building blocks used to construct the words by concatenation. Our approach, which…
In this paper, we consider the problem of avoiding a single vincular pattern of length three by derangements in the flattened sense and find explicit formulas for the generating functions enumerating members of each corresponding avoidance…
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…
Generalised polynomials are maps constructed by applying the floor function, addition, and multiplication to polynomials. Despite superficial similarity, generalised polynomials exhibit many phenomena which are impossible for polynomials.…
We determine the conditions for the existence or not of cycles for several families of generalized 3x + 1 mappings and develop a method to find them.
We enumerate permutations that avoid all but one of the $k$ patterns of length $k$ starting with a monotone increasing subsequence of length $k-1$. We compare the size of such permutation classes to the size of the class of permutations…
We discuss a new notion of pattern avoidance motivated by the operad theory: pattern avoidance in planar labelled trees. It is a generalisation of various types of consecutive pattern avoidance studied before: consecutive patterns in words,…
In previous papers, for an arithmetical function $f_0$, we defined functions $f_m$ and $c_m$ and designated numbers of restricted words over a finite alphabet counted by these functions. In this paper, we examine the reverse problem for…
Generating trees are a useful technique in the enumeration of various combinatorial objects, particularly restricted permutations. Quite often the generating tree for the set of permutations avoiding a set of patterns requires infinitely…
We use stack words to find a new, simple proof for the best known upper bound for the number of 3-stack sortable permutations of a given length. This is the first time that stack words are used to obtain such a result.
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…
This work is a continuation of some recent articles presenting enumerative results for Catalan words avoiding one or a pair of consecutive or classical patterns of length $3$. More precisely, we provide systematically the bivariate…
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 start by considering binary words containing the minimum possible numbers of squares and antisquares (where an antisquare is a word of the form $x \overline{x}$), and we completely classify which possibilities can occur. We consider…