DOAJ Open Access 2015

The $(m, n)$-rational $q, t$-Catalan polynomials for $m=3$ and their $q, t$-symmetry

Ryan Kaliszewski Huilan Li

Lihat Sumber DOI

Abstrak

We introduce a new statistic, skip, on rational $(3,n)$-Dyck paths and define a marked rank word for each path when $n$ is not a multiple of 3. If a triple of valid statistics (area; skip; dinv) are given, we have an algorithm to construct the marked rank word corresponding to the triple. By considering all valid triples we give an explicit formula for the $(m,n)$-rational $q; t$-Catalan polynomials when $m=3$. Then there is a natural bijection on the triples of statistics (area; skip; dinv) which exchanges the statistics area and dinv while fixing the skip. Thus we prove the $q; t$-symmetry of $(m,n)$-rational $q; t$-Catalan polynomials for $m=3$..

Topik & Kata Kunci

Mathematics

Penulis (2)

Ryan Kaliszewski

Huilan Li

Format Sitasi

APA MLA BibTeX

Kaliszewski, R., Li, H. (2015). The $(m, n)$-rational $q, t$-Catalan polynomials for $m=3$ and their $q, t$-symmetry. https://doi.org/10.46298/dmtcs.2500

Akses Cepat

Lihat di Sumber doi.org/10.46298/dmtcs.2500

Informasi Jurnal

Tahun Terbit: 2015
Sumber Database: DOAJ
DOI: 10.46298/dmtcs.2500
Akses: Open Access ✓