论文标题
大惊小怪的三个相互作用的家族
Three interacting families of Fuss-Catalan posets
论文作者
论文摘要
引入了三个家族的POSET家族，具体取决于非负整数参数$ M $。这些Posets的基础集由加泰罗尼亚$ M $ fuss的加泰罗尼亚人列举。其中，一个是史丹利晶格的概括，另一个是塔玛里晶格的概括。 POSET的三个家族是相关的：它们适合订单扩展关系的链，并具有一些属性。两个联想代数被构造为马尔维托鲁特纳列犬代数的概括的商。他们的产品描述了我们史丹利晶格和塔玛里晶格的类似物的间隔。特别是，一个是loday-ronco代数的概括。
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.
