Applications of residues to combinatorial identities

Huang, I-Chiau

doi:10.1090/S0002-9939-97-03923-3

Applications of residues to combinatorial identities
HTML articles powered by AMS MathViewer

by I-Chiau Huang PDF

Proc. Amer. Math. Soc. 125 (1997), 1011-1017 Request permission

Abstract:

A concrete aspect of Grothendieck Duality is used to give local cohomology proofs of combinatorial identities including MacMahon’s master theorem, Grosswald identity, identity of Shoo, Tepper identity, and others.

References

G. P. Egorychev, Integral representation and the computation of combinatorial sums, Translations of Mathematical Monographs, vol. 59, American Mathematical Society, Providence, RI, 1984. Translated from the Russian by H. H. McFadden; Translation edited by Lev J. Leifman. MR 736151, DOI 10.1090/mmono/059
I. J. Good, A short proof of MacMahon’s ‘Master Theorem’, Proc. Cambridge Philos. Soc. 58 (1962), 160. MR 137658, DOI 10.1017/s0305004100036318
I. P. Goulden and D. M. Jackson, Combinatorial enumeration, Wiley-Interscience Series in Discrete Mathematics, John Wiley & Sons, Inc., New York, 1983. With a foreword by Gian-Carlo Rota. MR 702512
I-Chiau Huang, Pseudofunctors on modules with zero-dimensional support, Mem. Amer. Math. Soc. 114 (1995), no. 548, xii+53. MR 1239604, DOI 10.1090/memo/0548
Ernst Kunz, Kähler differentials, Advanced Lectures in Mathematics, Friedr. Vieweg & Sohn, Braunschweig, 1986. MR 864975, DOI 10.1007/978-3-663-14074-0
Joseph Lipman, Dualizing sheaves, differentials and residues on algebraic varieties, Astérisque 117 (1984), ii+138 (English, with French summary). MR 759943
Hideyuki Matsumura, Commutative ring theory, Cambridge Studies in Advanced Mathematics, vol. 8, Cambridge University Press, Cambridge, 1986. Translated from the Japanese by M. Reid. MR 879273