Discrete Mathematics & Theoretical Computer Science |

2938

- 1 Department of Mathematics and Computer Science

Realisations of associahedra can be obtained from the classical permutahedron by removing some of its facets and the set of facets is determined by the diagonals of certain labeled convex planar $n$-gons as shown by Hohlweg and Lange (2007). Ardila, Benedetti, and Doker (2010) expressed polytopes of this type as Minkowski sums and differences of scaled faces of a standard simplex and computed the corresponding coefficients $y_I$ by Möbius inversion from the $z_I$ if tight right-hand sides $z_I$ for all inequalities of the permutahedron are assumed. Given an associahedron of Hohlweg and Lange, we first characterise all tight values $z_I$ in terms of non-crossing diagonals of the associated labeled $n$-gon, simplify the formula of Ardila et al., and characterise the remaining terms combinatorially.

Source: HAL:hal-01215039v1

Volume: DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)

Section: Proceedings

Published on: January 1, 2011

Imported on: January 31, 2017

Keywords: reflection and Coxeter groups,lattice polytopes,associahedra,Minkowski sums,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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