Discrete Mathematics & Theoretical Computer Science 
We introduce a "lifting'' construction for generalized permutohedra, which turns an $n$dimensional generalized permutahedron into an $(n+1)$dimensional one. We prove that this construction gives rise to Stasheff's multiplihedron from homotopy theory, and to the more general "nestomultiplihedra,'' answering two questions of Devadoss and Forcey. We construct a subdivision of any lifted generalized permutahedron whose pieces are indexed by compositions. The volume of each piece is given by a polynomial whose combinatorial properties we investigate. We show how this "composition polynomial'' arises naturally in the polynomial interpolation of an exponential function. We prove that its coefficients are positive integers, and conjecture that they are unimodal.
Source : ScholeXplorer
IsRelatedTo ARXIV math/0212126 Source : ScholeXplorer IsRelatedTo DOI 10.1007/s000130041026y Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.math/0212126
