# Welcome to the LaCIM

The Laboratoire de combinatoire et d'informatique mathématique (LaCIM) is an international research center based in Montreal, and gathers researchers in mathematics and computer science.

The main research interests of LaCIM's researchers are:

• combinatorics;
• algebraic combinatorics;
• bioinformatics;
• mathematical aspects of computer science.

# News

## LIRCO renewed for 4 years

The LIRCO, an international associated laboratory created in 2011 by the CNRS (France) has been renewed for another 4 years, from January 1st, 2015 to December 31st, 2018. The scientific representants are Mireille Bousquet-Mélou and Srečko Brlek.

## Award for scientific cooperation with France

Srĕcko Brlek, full professor of the Computer Sciences Department of Université du Québec à Montréal has been awarded the Acfas Prize - Adrien-Pouliot 2014, for scientific cooperation with France.

More details can be found on the Acfas website.

# Upcoming seminars

## Ramsey Theory on the Integers - Some Results and Conjectures on the Schur Numbers

### Tanbir Ahmed, Concordia University

Abstract: The Schur number $S(k)$ is the smallest positive integer $n$ such that for every $2$-colouring of $\{1,2,...,n\}$, there is a monochromatic solution to $x+y=z$ with $y \geq x$. In this talk, we discuss some computational aspects of Schur numbers and generalized Schur numbers, and also present some relevant results and conjectures.

## Combinatoire des polyominos dirigés k-convexes.

### Adrien Boussicault, Université de Bordeaux I

Résumé: Dans cet exposé, nous allons présenter une nouvelle bijection entre les polyominos parallélogrammes et les arbres binaires. Nous étendrons ensuite cette bijection afin d'obtenir une bijection simple entre chemins bilatères et polyominos dirigés convexes.

Nous utiliserons cette dernière construction pour obtenir facilement et instantanément les fonctions génératrices des polyominos dirigés convexes avec différentes combinaisons de statistiques : hauteur, largeur, longueur de la dernière ligne/colonne, nombre de coins. Nous énumérerons ensuite le cas difficile des polyominos dirigés $k$-convexes.

Il s'agit d'un travail réalisé en commun avec Simone Rinaldi et Samanta Socci de l'Université de Sienne en Italie.

## Generated Groups, Shellability, and Transitivity of the Hurwitz Action

### Henri Mühle, Université Paris Diderot – Paris 7

Abstract: Let $G$ be a group generated by a conjugation closed set $A$. There is a natural action of the braid group on $k$ strands on the set of reduced $A$-decompositions of any group element of length $k$, the Hurwitz action. It can informally be described as "shifting letters to the right, and conjugating as you go". Moreover, in the given setting we can naturally define a subword order on $G$, and it is immediate that the reduced $A$-decompositions of any group element are in bijection with the maximal chains in the principal order ideal generated by this element.

Using this perspective we present a new approach to proving the transitivity of the Hurwitz action, in that we establish a connection between the shellability of this subword order and the Hurwitz transitivity. This work (which is joint work with Vivien Ripoll from the University of Vienna) culminates in the observation that these two properties, whose proofs are in general far from being trivial, follow from a simple local criterion, namely the existence of a well-behaved total order of $A$.

Résumé: À venir.