The weak order on integer posets

DOI10.5802/alco.36OpenAlexW4297326074WikidataQ128451366 ScholiaQ128451366MaRDI QIDQ1726032

Grégory Chatel, Viviane Pons, Vincent Pilaud

Publication date: 15 February 2019

Published in: Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.07995

zbMATH Keywords

latticesweak orderinteger binary relations

Mathematics Subject Classification ID

Special polytopes (linear programming, centrally symmetric, etc.) (52B12) Combinatorics of partially ordered sets (06A07) Logical aspects of lattices and related structures (03G10) Lattices (06B99)

Related Items (9)

Permutree sorting ⋮ Algebraic structures on integer posets ⋮ The canonical complex of the weak order ⋮ Exceptional and modern intervals of the Tamari lattice ⋮ The Weak Order on Weyl Posets ⋮ P-flag spaces and incidence stratifications ⋮ The bounded derived categories of the Tamari lattices are fractionally Calabi-Yau ⋮ Combinatorics of quasi-hereditary structures ⋮ The Hopf algebra of integer binary relations

Uses Software

• SageMath
• OEIS
• Sage-Combinat

Cites Work

• Unnamed Item
• Associahedra, Tamari lattices and related structures. Tamari memorial Festschrift
• Construction of dendriform trialgebras.
• Permutation statistics and linear extensions of posets
• The singular locus of a Schubert variety
• Realization of the Stasheff polytope
• Counting smaller elements in the Tamari and \(m\)-Tamari lattices
• Realizations of the associahedron and cyclohedron
• Cambrian Hopf algebras
• Weak Bruhat order on the set of faces of the permutohedron and the associahedron.
• Cambrian lattices.
• Lattice congruences of the weak order.
• Quantization of Prior Probabilities for Collaborative Distributed Hypothesis Testing
• The facial weak order and its lattice quotients
• Permutrees

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