Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)
From generalized Tamari intervals to non-separable planar maps (extended abstract)
Wenjie Fang  1, 2  , Louis-François Préville-Ratelle  3  
1 : Institut de Recherche en Informatique Fondamentale  (IRIF)  -  Website
Université Paris Diderot - Paris 7, Centre National de la Recherche Scientifique : UMR8243
Université Paris-Diderot – Paris 7 Case 7014 75205 PARIS Cedex 13 -  France
2 : Laboratoire Bordelais de Recherche en Informatique  (LaBRI)  -  Website
Université Bordeaux Segalen - Bordeaux 2, Université Sciences et Technologies - Bordeaux 1, École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB), Centre National de la Recherche Scientifique : UMR5800
Domaine Universitaire 351, cours de la Libération 33405 Talence Cedex -  France
3 : Instituto de Matemática y Física - Universidad de Talca  -  Website
Universidad de Talca2 norte 685TalcaChile -  Chili

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.

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