Binomial residues  [ Résidus binomiaux ]
Annales de l'Institut Fourier, Tome 52 (2002) no. 3, pp. 687-708.

Un résidu binomial est une fonction rationnelle définie par une intégrale hypergéométrique ayant un noyau singulier le long d’un diviseur binomial. Les résidus binomiaux donnent une représentation intégrale des solutions rationnelles des systèmes A-hypergéométriques du type de Lawrence. L’espace des résidus binomiaux d’un degré donné, modulo ceux qui dépendent polynomialement d’une des variables, a sa dimension égale à la caractéristique d’Euler du matroïde associé à A.

A binomial residue is a rational function defined by a hypergeometric integral whose kernel is singular along binomial divisors. Binomial residues provide an integral representation for rational solutions of A-hypergeometric systems of Lawrence type. The space of binomial residues of a given degree, modulo those which are polynomial in some variable, has dimension equal to the Euler characteristic of the matroid associated with A.

DOI : https://doi.org/10.5802/aif.1898
Classification : 05B35,  14M25,  32A27
Mots clés: résidus binomiaux, fonctions hypergéométriques, configurations de Lawrence
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     author = {Cattani, Eduardo and Dickenstein, Alicia and Sturmfels, Bernd},
     title = {Binomial residues},
     journal = {Annales de l'Institut Fourier},
     pages = {687--708},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {52},
     number = {3},
     year = {2002},
     doi = {10.5802/aif.1898},
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     mrnumber = {1907384},
     language = {en},
     url = {aif.centre-mersenne.org/item/AIF_2002__52_3_687_0/}
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Cattani, Eduardo; Dickenstein, Alicia; Sturmfels, Bernd. Binomial residues. Annales de l'Institut Fourier, Tome 52 (2002) no. 3, pp. 687-708. doi : 10.5802/aif.1898. https://aif.centre-mersenne.org/item/AIF_2002__52_3_687_0/

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