DOAJ Open Access 2020

Minimal factorizations of a cycle: a multivariate generating function

Philippe Biane Matthieu Josuat-Vergès

Lihat Sumber DOI

Abstrak

It is known that the number of minimal factorizations of the long cycle in the symmetric group into a product of k cycles of given lengths has a very simple formula: it is nk−1 where n is the rank of the underlying symmetric group and k is the number of factors. In particular, this is nn−2 for transposition factorizations. The goal of this work is to prove a multivariate generalization of this result. As a byproduct, we get a multivariate analog of Postnikov's hook length formula for trees, and a refined enumeration of final chains of noncrossing partitions.

Topik & Kata Kunci

Mathematics

Penulis (2)

Philippe Biane

Matthieu Josuat-Vergès

Format Sitasi

APA MLA BibTeX

Biane, P., Josuat-Vergès, M. (2020). Minimal factorizations of a cycle: a multivariate generating function. https://doi.org/10.46298/dmtcs.6318

Akses Cepat

Lihat di Sumber doi.org/10.46298/dmtcs.6318

Informasi Jurnal

Tahun Terbit: 2020
Sumber Database: DOAJ
DOI: 10.46298/dmtcs.6318
Akses: Open Access ✓