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    Pavillon President-Kennedy, UQAM

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    ARTA III : Advances in representation theory of algebras (2014)

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    Mathematics in Marseille with Mark Haiman, Cédrik and François Bergeron

  • RS, Adriano Garsia
La Jolla, CA

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    Mathematics at the beach, Richard Stanley and Adriano Garsia (2003)

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    Mathematics at a bar in Banff with Adriano Garsia and Nantel Bergeron

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    Mountain mathematics with Francois and Nantel Bergeron, Jennifer Morse and Adriano Garsia

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    Welcome to LaCIM!

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    Gilbert Labelle and Christophe Reutenauer

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    Welcome to LaCIM!

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Welcome to LaCIM

The LaCIM  (Laboratoire de Combinatoire et d’Informatique Mathématique) is a research center gathering researchers, postdoctoral fellows, as well as graduate and undergraduate students interested in

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Seminars

A proof of the Delta conjecture for q = 0.Friday, 25 August 2017, 13:30

Adriano Garsia (University of California San Diego)

Abstract: In this talk we will present the basic ideas that led to a symmetric function proof of the Delta conjecture for $q = 0$. In a recent unpublished work Jim Haglund and Messue You prove that the Delta conjecture at $q = 0$ is equivalent to the validity of an equality of the form $A_{k;\lambda}(q) = B_{k;\lambda}(q)$ for all $\lambda \vdash n$ and $1 \le k \le n$. Our argument starts by showing that these identities are equivalent to symmetric function identities of the form $A_{k,n}(X; q) = B_{k,n}(X; q)$ for all $1 \le k \le n$. What is perhaps more important than the result itself is the introduction of a new method of proving symmetric function identities by means of multiple uses of Cauchy kernels.

$k$-abelian equivalence - an equivalence relation inbetween the equality and the abelian equalityFriday, 08 September 2017, 13:30

Juhani Karhumäki (Université de Turku)

Abstract: Two words $u$ and $v$ are $k$-abelian equivalent if, for each $w$ of length at most $k$, the number of occurrences of $w$ in $u$ coincides to that in $v$. The $k$-abelian equivalence is a natural equivalence relation, in fact a congruence, between the equality and the abelian equality. Topics we consider in this lecture are the avoidability of patterns, the palindromicity, and different types of complexity issues, in particular the number of the equivalence classes and the fluctuation of the complexity function of infinite words. We show that the set of minimal elements of the equivalence classes is a rational set. Consequently, for each parameter $k$ and alphabet size $m$, the numbers of equivalence classes of words of length $n$ form a rational sequence. Given $k$ and $m$ this sequence is algorithmically computable, but in practice only on very small values of the parameters.