Geodesic
Minkowski decompositions of associahedra
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) (2011).

Voir la notice de l'article provenant de la source Episciences

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. 
@article{DMTCS_2011_special_260_a51,
     author = {Lange, Carsten},
     title = {Minkowski decompositions of associahedra},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)},
     year = {2011},
     doi = {10.46298/dmtcs.2938},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2938/}
}
TY  - JOUR
AU  - Lange, Carsten
TI  - Minkowski decompositions of associahedra
JO  - Discrete mathematics & theoretical computer science
PY  - 2011
VL  - DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2938/
DO  - 10.46298/dmtcs.2938
LA  - en
ID  - DMTCS_2011_special_260_a51
ER  - 
%0 Journal Article
%A Lange, Carsten
%T Minkowski decompositions of associahedra
%J Discrete mathematics & theoretical computer science
%D 2011
%V DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2938/
%R 10.46298/dmtcs.2938
%G en
%F DMTCS_2011_special_260_a51
Lange, Carsten. Minkowski decompositions of associahedra. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) (2011). doi : 10.46298/dmtcs.2938. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2938/

Cité par Sources :