A Heyting algebra on Dyck paths of type \(A\) and \(B\)

DOI10.1007/s11083-016-9403-2zbMath1392.06006arXiv1312.0551OpenAlexW1539981675MaRDI QIDQ2407687

Henri Mühle

Publication date: 6 October 2017

Published in: Order (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.0551

zbMATH Keywords

symmetric groupDyck pathdistributive latticeHeyting algebrahyperoctahedral groupCatalan numbersdominance order

Mathematics Subject Classification ID

Combinatorics of partially ordered sets (06A07) Heyting algebras (lattice-theoretic aspects) (06D20) Structure and representation theory of distributive lattices (06D05)

Related Items (2)

The rank enumeration of certain parabolic non-crossing partitions ⋮ Dyck Algebras, Interval Temporal Logic, and Posets of Intervals

Cites Work

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• Lattices of paths: representation theory and valutions
• Enumeration of chains and saturated chains in Dyck lattices.
• Noncrossing partitions and Bruhat order
• Dyck path enumeration
• Two families of Newman lattices
• The matrix of chromatic joins and the Temperley-Lieb algebra.
• Lattices and ordered algebraic structures
• Bruhat lattices, plane partition generating functions, and minuscule representations
• More bijective Catalan combinatorics on permutations and on signed permutations
• A distributive lattice structure connecting Dyck paths, noncrossing partitions and 312-avoiding permutations
• Lattices of lattice paths
• Noncrossing partitions, fully commutative elements and bases of the Temperley–Lieb algebra
• Dyck Algebras, Interval Temporal Logic, and Posets of Intervals
• Generalized noncrossing partitions and combinatorics of Coxeter groups
• Weyl Groups, the Hard Lefschetz Theorem, and the Sperner Property
• Unimodality and Dyck paths
• Enumeration of basic ideals in type B
• Enumeration of edges in some lattices of paths

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