DOAJ
Open Access
2014
An extension of MacMahon's Equidistribution Theorem to ordered multiset partitions
Andrew Timothy Wilson
Abstrak
A classical result of MacMahon states that inversion number and major index have the same distribution over permutations of a given multiset. In this work we prove a strengthening of this theorem originally conjectured by Haglund. Our result can be seen as an equidistribution theorem over the ordered partitions of a multiset into sets, which we call ordered multiset partitions. Our proof is bijective and involves a new generalization of Carlitz's insertion method. As an application, we develop refined Macdonald polynomials for hook shapes. We show that these polynomials are symmetric and give their Schur expansion.
Topik & Kata Kunci
Penulis (1)
A
Andrew Timothy Wilson
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2014
- Sumber Database
- DOAJ
- DOI
- 10.46298/dmtcs.2405
- Akses
- Open Access ✓