Problems of associativity: A simple proof for the lattice property of systems ordered by a semi-associative law
Samuel Huang,Dov Tamari +1 more
TLDR
A short proof of the lattice property of (Tn, →), the system of binary bracketings ordered by a semi-associative law, is presented.About:
This article is published in Journal of Combinatorial Theory, Series A.The article was published on 1972-07-01 and is currently open access. It has received 137 citations till now. The article focuses on the topics: Tamari lattice & Associative property.read more
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Lattice Theory: Foundation
TL;DR: In this paper, the authors define two definitions of lattices and describe how to describe lattices, including terms, identities, and inequalities, as well as constructions of lattice constructions.
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Shellable nonpure complexes and posets. II
Anders Björner,Michelle L. Wachs +1 more
TL;DR: In this paper, the applicability of lexicographic shellability to nonpure posets is discussed, and an edge-labeling λ of L(F) is defined as follows.
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Intervals in Catalan lattices and realizers of triangulations
TL;DR: It is proved that @F induces a bijection between Tamari intervals and minimal realizers and Kreweras intervals and stack triangulations which are known to be in bijection with ternary trees.
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Primes, irreducibles and extremal lattices
TL;DR: In this paper, it was shown that lattices which are long enough must have primes and coprimes and that these elements and the resulting decompositions can be used to study such lattices.
References
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Problèmes d'associativité: Une structure de treillis finis induite par une loi demi-associative
Haya Friedman,Dov Tamari +1 more
TL;DR: In this article, the authors propose a systeme ordonnes finis, in which a set of parenthesages and transformations of monomes non-associatifs are organized in a system.