Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8903635 | European Journal of Combinatorics | 2018 | 18 Pages |
Abstract
We consider quotients of the unit cube semigroup algebra by particular ZrâSn-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 (Ï,ϵ)âZrâSn and each element encodes the negative descent and negative major index statistics on (Ï,ϵ). This gives an algebraic interpretation of these statistics that was previously unknown. This basis of the ZrâSn-quotients allows us to recover certain combinatorial identities involving Euler-Mahonian distributions of statistics.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Benjamin Braun, McCabe Olsen,