DOAJ Open Access 2020

From generalized Tamari intervals to non-separable planar maps

Wenjie Fang Louis-François Préville-Ratelle

Lihat Sumber DOI

Abstrak

Let v be a grid path made of north and east steps. The lattice TAM(v), based on all grid paths weakly above the grid path v sharing the same endpoints as v, was introduced by Pre ́ville-Ratelle and Viennot (2014) and corresponds to the usual Tamari lattice in the case v = (NE)n. They showed that TAM(v) is isomorphic to the dual of TAM(←−v ), where ←−v is the reverse of v with N and E exchanged. Our main contribution is a bijection from intervals in TAM(v) to non-separable planar maps. It follows that the number of intervals in TAM(v) over all v of length n is 2(3n+3)! (n+2)!(2n+3)! . This formula was first obtained by Tutte(1963) for non-separable planar maps.

Topik & Kata Kunci

Mathematics

Penulis (2)

Wenjie Fang

Louis-François Préville-Ratelle

Format Sitasi

APA MLA BibTeX

Fang, W., Préville-Ratelle, L. (2020). From generalized Tamari intervals to non-separable planar maps. https://doi.org/10.46298/dmtcs.6421

Akses Cepat

Lihat di Sumber doi.org/10.46298/dmtcs.6421

Informasi Jurnal

Tahun Terbit: 2020
Sumber Database: DOAJ
DOI: 10.46298/dmtcs.6421
Akses: Open Access ✓