Related papers: Combinatorial distance between braid words

In this paper, we establish a fundamental connection between binomial parameters and means of bounded random variables. Such connection finds applications in statistical inference of means of bounded variables.

We construct small models of number fields and deduce a better bound for the number of number fields of given degree and bounded discriminant.

Dihedral codes, particular cases of quasi-cyclic codes, have a nice algebraic structure which allows to store them efficiently. In this paper, we investigate it and prove some lower bounds on their dimension and minimum distance, in analogy…

We use a probabilistic method to produce some combinatorial inequalities by considering pattern containment in permutations and words.

We develop a combinatorial approach to the study of semigroups and monoids with finite presentations satisfying small overlap conditions. In contrast to existing geometric methods, our approach facilitates a sequential left-right analysis…

Given a fixed number field K, we give non-trivial lower bounds for the distance between the conjugates of any number a from K in terms of the Mahler measure M(a) of a. In the case that K is a cubic field, our bound is best possible in terms…

The norm distance between two composition operators is calculated in select cases.

We obtain lower bound for the maximum distance between any three distinct points in an affine lattice which are close to a helix with small curvature and torsion.

We construct long sequences of braids that are descending with respect to the standard order of braids (``Dehornoy order''), and we deduce that, contrary to all usual algebraic properties of braids, certain simple combinatorial statements…

We develop combinatorial methods for computing the rotation distance between binary trees, i.e., equivalently, the flip distance between triangulations of a polygon. As an application, we prove that, for each n, there exist size n trees at…

We investigate a class of combinatory algebras, called ribbon combinatory algebras, in which we can interpret both the braided untyped linear lambda calculus and framed oriented tangles. Any reflexive object in a ribbon category gives rise…

Many interesting families of polynomials are indexed by permutations or related objects, and are defined by applying divided difference operators, modified by polynomials, on some initial base case. The fact that these constructions produce…

Grammatical relationships (GRs) form an important level of natural language processing, but different sets of GRs are useful for different purposes. Therefore, one may often only have time to obtain a small training corpus with the desired…

We obtain a series of lower bounds for the product set of combinatorial cubes, as well as some non--trivial upper estimates for the multiplicative energy of such sets.

I will show that there exist two binary words (one of length 4 and one of length 6) that play a special role in many different problems in combinatorics on words. They can therefore be considered \textit{the shortest interesting binary…

We generalize presentations of the fundamental group of discriminant complements and arrive at a class of presentations associated naturally with words in the free monoid of the alphabet $\sigma_1,\dots,\sigma_{n-1}$. Our study addresses…

We show that the problem of constructing a real rational knot of a reasonably low degree can be reduced to an algebraic problem involving the pure braid group: expressing an associated element of the pure braid group in terms of the…

The palindromic length of the finite word $v$ is equal to the minimal number of palindromes whose concatenation is equal to $v$. It was conjectured in 2013 that for every infinite aperiodic word $x$, the palindromic length of its factors is…

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.

We prove a number of results on the structure and enumeration of palindromes and antipalindromes. In particular, we study conjugates of palindromes, palindromic pairs, rich words, and the counterparts of these notions for antipalindromes.