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- W2414895788 abstract "We consider quotients of the unit cube semigroup algebra by particular $mathbb{Z}_rwr S_n$-invariant ideals. Using Grobner basis methods, we show that the resulting graded quotient algebra has a basis where each element is indexed by colored permutations $(pi,epsilon)inmathbb{Z}_rwr S_n$ and each element encodes the negative descent and negative major index statistics on $(pi,epsilon)$. This gives an algebraic interpretation of these statistics which was previously unknown. This basis of the $mathbb{Z}_rwr S_n$-quotients allows us to recover certain combinatorial identities involving Euler-Mahonian distributions of statistics." @default.
- W2414895788 created "2016-06-24" @default.
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- W2414895788 date "2016-06-09" @default.
- W2414895788 modified "2023-09-27" @default.
- W2414895788 title "Euler-Mahonian statistics and descent bases for semigroup algebras" @default.
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