DOAJ Open Access 2009

Matrix Ansatz, lattice paths and rook placements

S. Corteel M. Josuat-Vergès T. Prellberg M. Rubey

Lihat Sumber DOI

Abstrak

We give two combinatorial interpretations of the Matrix Ansatz of the PASEP in terms of lattice paths and rook placements. This gives two (mostly) combinatorial proofs of a new enumeration formula for the partition function of the PASEP. Besides other interpretations, this formula gives the generating function for permutations of a given size with respect to the number of ascents and occurrences of the pattern $13-2$, the generating function according to weak exceedances and crossings, and the $n^{\mathrm{th}}$ moment of certain $q$-Laguerre polynomials.

Topik & Kata Kunci

Mathematics

Penulis (4)

S. Corteel

M. Josuat-Vergès

T. Prellberg

M. Rubey

Format Sitasi

APA MLA BibTeX

Corteel, S., Josuat-Vergès, M., Prellberg, T., Rubey, M. (2009). Matrix Ansatz, lattice paths and rook placements. https://doi.org/10.46298/dmtcs.2751

Akses Cepat

Lihat di Sumber doi.org/10.46298/dmtcs.2751

Informasi Jurnal

Tahun Terbit: 2009
Sumber Database: DOAJ
DOI: 10.46298/dmtcs.2751
Akses: Open Access ✓