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- W2968738962 abstract "We describe a perturbation method that can be used to compute the multivariate generating function (MGF) of a non-simple polyhedron, and then construct a perturbation that works for any transportation polytope. Applying this perturbation to the family of central transportation polytopes of order $kn times n$, we obtain formulas for the MGF of the polytope. The formulas we obtain are enumerated by combinatorial objects. A special case of the formulas recovers the results on Birkhoff polytopes given by the author and De Loera and Yoshida. We also recover the formula for the number of maximum vertices of transportation polytopes of order $kn times n$. Nous décrivons une méthode de perturbation qui peut être utilisée pour calculer la fonction génératrice multivariée (MGF) d'un polyèdre non-simple, et ensuite construire une perturbation qui fonctionne pour tout polytope de transport. Appliquant cette perturbation à la famille des centraux de transport polytopes de l'ordre $kn times n$, nous obtenons des formules pour le MGF du polytope. Les formules que nous obtenons sont énumérées par les objets combinatoires. Un cas spécial des formules récupère les résultats sur des polytopes de Birkhoff donnés par l'auteur et De Loera et Yoshida. Nous récupérons également la formule pour le nombre de sommets maximum des de transport polytopes d'ordre $kn times n$." @default.
- W2968738962 created "2019-08-22" @default.
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- W2968738962 date "2012-01-01" @default.
- W2968738962 modified "2023-09-25" @default.
- W2968738962 title "Perturbation of transportation polytopes" @default.
- W2968738962 doi "https://doi.org/10.46298/dmtcs.3097" @default.
- W2968738962 hasPublicationYear "2012" @default.
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