Topic
Tamari lattice
About: Tamari lattice is a research topic. Over the lifetime, 114 publications have been published within this topic receiving 1548 citations.
Papers published on a yearly basis
Papers
Journal Article•
TL;DR: In this article, the authors enumerate the intervals in the Tamari lattices and define a notion of new interval, which is defined by a tree-indexed series, and then these are also enumerated.
Abstract: We enumerate the intervals in the Tamari lattices. For this, we introduce an inductive description of the intervals. Then a notion of "new interval" is defined and these are also enumerated. As a side result, the inverse of two special series is computed in a group of tree-indexed series.
64 citations
TL;DR: In this article, it was shown that the number of labelledm-Tamari intervals of s-ballot paths is (m + 1) n (mn + 1/n 2 ) for any constant m = 1.
52 citations
TL;DR: In this paper, a class of Garside groupoid structures on pure braid groups, one for each function (called labelling) from the punctures to the integers greater than 1, was constructed.
Abstract: We construct a class of Garside groupoid structures on the pure braid groups, one for each function (called labelling) from the punctures to the integers greater than 1. The object set of the groupoid is the set of ball decompositions of the punctured disk; the labels are the perimeters of the regions. Our construction generalises Garside's original Garside structure, but not the one by Birman-Ko-Lee. As a consequence, we generalise the Tamari lattice ordering on the set of vertices of the associahedron.
47 citations
TL;DR: In this paper, the authors trace the path from the Tamari lattice, via lattice congruences of the weak order, to the definition of Cambrian lattices in the context of finite Coxeter groups, and onward to the construction of the Cambrian fans.
Abstract: We trace the path from the Tamari lattice, via lattice congruences of the weak order, to the definition of Cambrian lattices in the context of finite Coxeter groups, and onward to the construction of Cambrian fans. We then present sortable elements, the key combinatorial tool for studying Cambrian lattices and fans. The chapter concludes with a brief description of the applications of Cambrian lattices and sortable elements to Coxeter-Catalan combinatorics and to cluster algebras.
46 citations
Posted Content•
TL;DR: A combinatorial Hopf algebra dRec with basis elements indexed by diagonal rectangulations of a square is defined and an explicit bijection between twisted Baxter permutations and the better-known Baxter permutation is given, and the resulting Hopfgebra structure on Baxter perm mutations is described.
Abstract: We define and study a combinatorial Hopf algebra dRec with basis elements indexed by diagonal rectangulations of a square. This Hopf algebra provides an intrinsic combinatorial realization of the Hopf algebra tBax of twisted Baxter permutations, which previously had only been described extrinsically as a sub Hopf algebra of the Malvenuto-Reutenauer Hopf algebra of permutations. We describe the natural lattice structure on diagonal rectangulations, analogous to the Tamari lattice on triangulations, and observe that diagonal rectangulations index the vertices of a polytope analogous to the associahedron. We give an explicit bijection between twisted Baxter permutations and the better-known Baxter permutations, and describe the resulting Hopf algebra structure on Baxter permutations.
45 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 3 |
| 2020 | 6 |
| 2019 | 3 |
| 2018 | 17 |
| 2017 | 11 |
| 2016 | 3 |