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arXiv · 2002.09932

Three interacting families of Fuss-Catalan posets

Camille Combe·Samuele Giraudo
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Abstract

Three families of posets depending on a nonnegative integer parameter $m$ are introduced. The underlying sets of these posets are enumerated by the $m$-Fuss Catalan numbers. Among these, one is a generalization of Stanley lattices and another one is a generalization of Tamari lattices. The three families of posets are related: they fit into a chain for the order extension relation and they share some properties. Two associative algebras are constructed as quotients of generalizations of the Malvenuto-Reutenauer algebra. Their products describe intervals of our analogues of Stanley lattices and Tamari lattices. In particular, one is a generalization of the Loday-Ronco algebra.

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Camille Combe, Samuele Giraudo. 2020-02-23. Three interacting families of Fuss-Catalan posets. https://arxiv.org/abs/2002.09932

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