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تسجيل مستخدم جديدThree interacting families of Fuss-Catalan posets
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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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We introduce $delta$-cliffs, a generalization of permutations and increasing trees depending on a range map $delta$. We define a first lattice structure on these objects and we establish general results about its subposets. Among them, we describe su
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