Counting smaller elements in the Tamari and \(m\)-Tamari lattices

DOI10.1016/j.jcta.2015.03.004zbMath1315.05143arXiv1311.3922OpenAlexW2055446253MaRDI QIDQ2347970

Viviane Pons, Grégory Chatel

Publication date: 10 June 2015

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.3922

zbMATH Keywords

binary treesTamari latticeTamari intervals

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Combinatorial aspects of representation theory (05E10) Combinatorics of partially ordered sets (06A07)

Related Items (15)

The rise-contact involution on Tamari intervals ⋮ Ungarian Markov chains ⋮ Geometric realizations of Tamari interval lattices via cubic coordinates ⋮ Composition closed premodel structures and the Kreweras lattice ⋮ Exceptional and modern intervals of the Tamari lattice ⋮ The weak order on integer posets ⋮ A recursion on maximal chains in the Tamari lattices ⋮ Bijective link between Chapoton's new intervals and bipartite planar maps ⋮ The bounded derived categories of the Tamari lattices are fractionally Calabi-Yau ⋮ Cubic realizations of Tamari interval lattices ⋮ Combinatorics of quasi-hereditary structures ⋮ Meeting covered elements in \(\nu\)-Tamari lattices ⋮ \(N_\infty \)-operads and associahedra ⋮ Structure theorems for dendriform and tridendriform algebras ⋮ The Hopf algebra of integer binary relations

Uses Software

• SageMath
• FindStat

Cites Work

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• The algebra of binary search trees
• The number of intervals in the \(m\)-Tamari lattices
• Permutation statistics and linear extensions of posets
• Hopf algebra of the planar binary trees
• Higher trivariate diagonal harmonics via generalized Tamari posets
• Problems of associativity: a simple proof for the lattice property of systems ordered by a semi-associative law
• On the number of intervals in Tamari lattices
• Flows on Rooted Trees and the Menous-Novelli-Thibon Idempotents

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