Noncommutative inclusion–exclusion, representations of left regular bands and the Tsetlin library

Author:

Blachar Guy1,Rowen Louis H.1,Vishne Uzi1

Affiliation:

1. Department of Mathematics, Bar-Ilan University, Ramat-Gan 5290002, Israel

Abstract

We find a semigroup [Formula: see text], whose category of partial representations contains the representation category [Formula: see text] of the free left regular band [Formula: see text]. We use this to construct a resolution for the absolute kernel of a representation of [Formula: see text], for which the kernel [Formula: see text] of the Markov operation in the Tsetlin library model is a prominent example. We obtain a formula for the dimension of the absolute kernel, generalizing the equality of the dimension of [Formula: see text] to the number of derangements of order [Formula: see text].

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

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