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- W2963076862 abstract "In this article we introduce the $m$-cover poset of an arbitrary bounded poset $mathcal{P}$, which is a certain subposet of the $m$-fold direct product of $mathcal{P}$ with itself. Its ground set consists of multichains of $mathcal{P}$ that contain at most three different elements, one of which has to be the least element of $mathcal{P}$, and the other two elements have to form a cover relation in $mathcal{P}$. We study the $m$-cover poset from a structural and topological point of view. In particular, we characterize the posets whose $m$-cover poset is a lattice for all $m>0$, and we characterize the special cases, where these lattices are EL-shellable, left-modular, or trim. Subsequently, we investigate the $m$-cover poset of the Tamari lattice $mathcal{T}_{n}$, and we show that the smallest lattice that contains the $m$-cover poset of $mathcal{T}_{n}$ is isomorphic to the $m$-Tamari lattice $mathcal{T}_{n}^{(m)}$ introduced by Bergeron and Preville-Ratelle. We conclude this article with a conjectural desription of an explicit realization of $mathcal{T}_{n}^{(m)}$ in terms of $m$-tuples of Dyck paths." @default.
- W2963076862 created "2019-07-30" @default.
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- W2963076862 date "2013-12-09" @default.
- W2963076862 modified "2023-09-25" @default.
- W2963076862 title "The $m$-Cover Posets and the Strip-Decomposition of $m$-Dyck Paths" @default.
- W2963076862 hasPublicationYear "2013" @default.
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