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- W2142389211 abstract "An extension of the Tamari lattice to the multiplihedra is discussed, along with projections to the composihedra and the Boolean lattice. The multiplihedra and composihedra are sequences of polytopes that arose in algebraic topology and category theory. Here we describe them in terms of the composition of combinatorial species. We define lattice structures on their vertices, indexed by painted trees, which are extensions of the Tamari lattice and projections of the weak order on the permutations. The projections from the weak order to the Tamari lattice and the Boolean lattice are shown to be different from the classical ones. We review how lattice structures often interact with the Hopf algebra structures, following Aguiar and Sottile who discovered the applications of Möbius inversion on the Tamari lattice to the Loday-Ronco Hopf algebra." @default.
- W2142389211 created "2016-06-24" @default.
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- W2142389211 date "2012-01-01" @default.
- W2142389211 modified "2023-09-25" @default.
- W2142389211 title "Extending the Tamari Lattice to Some Compositions of Species" @default.
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- W2142389211 doi "https://doi.org/10.1007/978-3-0348-0405-9_10" @default.
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