Federico Ardila ; Jeffrey Doker - Lifted generalized permutahedra and composition polynomials

dmtcs:3094 - Discrete Mathematics & Theoretical Computer Science, January 1, 2012, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) - https://doi.org/10.46298/dmtcs.3094
Lifted generalized permutahedra and composition polynomialsArticle

Authors: Federico Ardila 1; Jeffrey Doker 2

  • 1 Department of Mathematics [San Francisco]
  • 2 Department of Mathematics [Berkeley]

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.


Volume: DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
Section: Proceedings
Published on: January 1, 2012
Imported on: January 31, 2017
Keywords: permutohedron, associahedron, multiplihedron, nestohedron, subdivision, composition polynomial, polynomial interpolation,Polytope,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • CAREER: Matroids, polytopes, and their valuations in algebra and geometry; Funder: National Science Foundation; Code: 0956178
  • Combinatorics in Geometry; Funder: National Science Foundation; Code: 0801075

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