Euler–Mahonian statistics and descent bases for semigroup algebras. (March 2018)

• Record Type: Journal Article
• Authors: Braun, Benjamin; Olsen, McCabe
• Is Part Of: European journal of combinatorics. Volume 69(2018)
• Page Start: 237
• Page End: 254
• Publication Date: 2018-03
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2017.11.005
• Languages: English
• ISSNs: 0195-6698

Abstract

Abstract: We consider quotients of the unit cube semigroup algebra by particular Z r ≀ S n -invariant ideals. Using Gröbner basis methods, we show that the resulting graded quotient algebra has a basis where each element is indexed by colored permutations ( π, ϵ ) ∈ Z r ≀ S n and each element encodes the negative descent and negative major index statistics on ( π, ϵ ) . This gives an algebraic interpretation of these statistics that was previously unknown. This basis of the Z r ≀ S n -quotients allows us to recover certain combinatorial identities involving Euler–Mahonian distributions of statistics.