Noncommutative Catalan numbers

Sun, 22/10/2017 - 14:00
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The goal of my talk (based on joint work with Vladimir Retakh) is to introduce and study noncommutative versions of Catalan numbers which belong to the free Laurent polynomial algebra L_n in n generators.  

Our noncommutative Catalan numbers C_n admit interesting (commutative and noncommutative) specializations, one of them related to  Garsia-Haiman (q,t)-versions, another -- to solving noncommutative 

quadratic equations.  We also establish total positivity of the corresponding (noncommutative) Hankel matrices H_n and introduce two kinds of noncommutative binomial coefficients which are instrumental 

in computing the inverse of H_n and in other combinatorial identities involving C_n.