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Communication Dans Un Congrès Année : 2021

Skew metrics valued in Sugihara semigroups

Résumé

We consider skew metrics (equivalently, transitive relations that are tournaments, linear orderings) valued in Sugihara semigroups on autodual chains. We prove that, for odd chains and chains without a unit, skew metrics classify certain tree-like structures that we call perfect augmented plane towers. When the chain is finite and has cardinality 2K + 1, skew metrics on a set X give rise to perfect rooted plane trees of height K whose frontier is a linear preorder of X. Any linear ordering on X gives rise to an ordering on the set of its skew metrics valued in an arbitrary involutive residuated lattice Q. If Q satisfies the mix rule, then this poset is most often a lattice. We study this lattice for X = {1,...,n} and Q the Sugihara monoid on the chain of cardinality 2K + 1. We give a combinatorial model of this lattice by de- scribing its covers as moves on a space of words coding perfect augmented plane trees. Using the combinatorial model, we develop enumerative considerations on this lattice.

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Dates et versions

hal-03518407 , version 1 (09-01-2022)

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  • HAL Id : hal-03518407 , version 1

Citer

Luigi Santocanale. Skew metrics valued in Sugihara semigroups. Relational and Algebraic Methods in Computer Science, Feb 2021, Marseille, France. pp.396--412. ⟨hal-03518407⟩
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