שלחו לחבר

Noncommutative Catalan numbers

Seminar
Speaker
Arkady Berenstein (U Oregon)
Date
22/10/2017 - 15:30 - 14:00
Place
(Room 201 , Math and CS Building (Bldg. 216 Seminar Room
Abstract

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.

תאריך עדכון אחרון : 17/10/2017