arXiv subjects

Srečko Brlek

Publications and source records attributed to Srečko Brlek.

8 recordsLinked to original sources

arXiv2026

Proceedings of the 14th edition of the conference on Random Generation of Combinatorial Structures

This volume contains the proceedings of GASCom 2026, held on June 8-12 2026, in Malosco (Italy). This series of conferences brings together researchers in combinatorics, algorithms, probabilities, and more generally mathematical computer science, around the theme of random and exhaustive generation of combinatorial structures, mostly considered from a theoretical point of view. In connection with this main theme, contributions in enumerative or analytic combinatorics, and interactions with other areas of mathematics, computer science, physics or biology are wellcome. The topics cover both the methods for random or exhaustive generation, and original results on combinatorial or algorithmic problems, whose solution has been made possible by an approach involving random or exhaustive generation. A (non exhaustive) list of topics of the conference is: random and exhaustive generation of combinatorial objects; tilings and polyominoes; bijective, enumerative, algebraic and analytic combinatorics; algorithmic aspects: analysis of algorithms, probabilistic algorithms; interactions: bio-informatics, combinatorics on words, number theory.

cs.DM↗

arXiv2024

Proceedings of the 13th edition of the conference on Random Generation of Combinatorial Structures. Polyominoes and Tilings

The conference GASCom brings together researchers in combinatorics, algorithms, probabilities, and more generally mathematical computer science, around the theme of random and exhaustive generation of combinatorial structures, mostly considered from a theoretical point of view. In connection with this main theme, the conference is also interested in contributions in enumerative or analytic combinatorics, and interactions with other areas of mathematics, computer science, physics or biology. The conference is both interested in methods for random or exhaustive generation and in original results on combinatorial or algorithmic questions, whose solution has been made possible by an approach involving random or exhaustive generation. The present edition of the conference includes a specific bunch of talks dedicated to polyominoes and tilings. A (not exhaustive) list of topics of the conference is: random and exhaustive generation of combinatorial objects; tilings and polyominoes; bijective, enumerative, algebraic and analytic combinatorics; algorithmic aspects: analysis of algorithms, probabilistic algorithms; interactions: bio-informatics, combinatorics on words, number theory.

cs.DM↗

arXiv2022

On the number of squares in a finite word

A {\em square} is a word of the form $uu$. In this paper we prove that for a given finite word $w$, the number of distinct square factors of $w$ is bounded by $|w|-|\Alphabet(w)|+1$, where $|w|$ denotes the length of $w$ and $|\Alphabet(w)|$ denotes the number of distinct letters in $w$. This result answers a conjecture of Fraenkel and Simpson stated in 1998.

math.CO↗

arXiv2015

Palindromic complexity of trees

We consider finite trees with edges labeled by letters on a finite alphabet $\varSigma$. Each pair of nodes defines a unique labeled path whose trace is a word of the free monoid $\varSigma^*$. The set of all such words defines the language of the tree. In this paper, we investigate the palindromic complexity of trees and provide hints for an upper bound on the number of distinct palindromes in the language of a tree.

math.CO↗

arXiv2011

Combinatorial Variations on Cantor's Diagonal

We discuss counting problems linked to finite versions of Cantor's diagonal of infinite tableaux. We extend previous results of [2] by refining an equivalence relation that reduces significantly the exhaustive generation. New enumerative results follow and allow to look at the sub-class of the so- called bi-Cantorian tableaux. We conclude with a correspondence between Cantorian-type tableaux and coloring of hypergraphs having a square number of vertices.

math.CO↗

arXiv2011

Interactions between Digital Geometry and Combinatorics on Words

We review some recent results in digital geometry obtained by using a combinatorics on words approach to discrete geometry. Motivated on the one hand by the well-known theory of Sturmian words which model conveniently discrete lines in the plane, and on the other hand by the development of digital geometry, this study reveals strong links between the two fields. Discrete figures are identified with polyominoes encoded by words. The combinatorial tools lead to elegant descriptions of geometrical features and efficient algorithms. Among these, radix-trees are useful for efficiently detecting path intersection, Lyndon and Christoffel words appear as the main tools for describing digital convexity; equations on words allow to better understand tilings by translations.

cs.CG↗

arXiv2011

Complexity of the Fibonacci snowflake

The object under study is a particular closed curve on the square lattice $\Z^2$ related with the Fibonacci sequence $F_n$. It belongs to a class of curves whose length is $4F_{3n+1}$, and whose interiors by translation tile the plane. The limit object, when conveniently normalized, is a fractal line for which we compute first the fractal dimension, and then give a complexity measure.

math.MG↗

arXiv2003

Cantorian Tableaux and Permanents

This article could be called "theme and variations" on Cantor's celebrated diagonal argument. Given a square nxn tableau T=(a_i^j) on a finite alphabet A, let L be the set of its row-words. The permanent Perm(T) is the set of words a_{π(1)}^1 a_{π(2)}^2 ...a_{π(n)}^n, where πruns through the set of permutations of n elements. Cantorian tableaux are those for which Perm(T)\cap L=\emptyset. Let s=s(n) be the cardinality of A. We show in particular that for large n, if s(n) <(1-ε) n/log n then most of the tableaux are non-Cantorian, whereas if s(n) >(1+ε) n/log n then most of the tableaux are Cantorian. We conclude our article by the study of infinite tableaux. Consider for example the infinite tableaux whose rows are the binary expansions of the real algebraic numbers in the unit interval. We show that the permanent of this tableau contains exactly the set of binary expansions of all the transcendental numbers in the unit interval.

math.CO↗