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Discrete Mathematics & Theoretical Computer Science |
Wenjie Fang ; Louis-François Préville-Ratelle - From generalized Tamari intervals to non-separable planar maps
dmtcs:6421 - Discrete Mathematics & Theoretical Computer Science, April 22, 2020, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) - https://doi.org/10.46298/dmtcs.6421
1,2; Louis-François Préville-Ratelle 3
- 1 Institut de Recherche en Informatique Fondamentale
- 2 Laboratoire Bordelais de Recherche en Informatique
- 3 Instituto de Matemática y Física - Universidad de Talca
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.