Alternating patterns in commutator monomials

Abstract

Considering commutator monomials of the non-commutative associative variables $X_1,\dots ,X_n$; we determine the maximal possible number of alternating associative monomials in their noncommutative polynomial expansions. This is achieved by replacing generating functions with polytope sequences, which turn out to be finitely generated in some sense.

arXiv comment18 pages