Abstract
We interpret the Combinatorial Nullstellensatz of Noga Alon as a multidimensional residue formula, describe some consequences of this interpretation and related open problems.
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References
N. Alon, Combinatorial Nullstellensatz. Comb. Probab. Comput. 8, 7–29 (1999)
I. Bacharach, Über den Cayley’schen schnittpunktsatz. Mathematische Annalen 26, 275–299 (1886)
G. Blekherman, Nonnegative polynomials and sums of squares (2010). arXiv:1010.3465
A. Cayley, On the Intersection of Curves (Cambridge University Press, Cambridge, 1889)
D. Eisenbud, M. Green, J. Harris, Cayley–Bacharach theorems and conjectures. Bull. Am. Math. Soc. 33, 295–324 (1996)
Z. Füredi, M. Ruszinkó, Uniform hypergraphs containing no grids (2011). arXiv:1103.1691
V. Gasca, T. Sauer, Polynomial interpolation in several variables. Adv. Comput. Math. 12, 377–410 (2000)
O.F. Gelfond, A.G. Khovanskii, Toric geometry and Grothendieck residues. Mosc. Math. J. 2(1), 99–112 (2002)
B. Green, T. Tao, On sets defining few ordinary lines (2012). arXiv:1208.4714
P. Griffiths, J. Harris, Principles of Algebraic Geometry. Cited by Vol. 2 of the Russian Edition (Wiley, New York, Chichester, Brisbane, Toronto, 1978)
R. Karasev, F. Petrov, Partitions of nonzero elements of a finite field into pairs. Isr. J. Math. 192, 143–156 (2012)
G. Károlyi, A. Lascoux, S. Ole Warnaar, Constant term identities and Poincaré polynomials (2012). arXiv:1209.0855
G. Károlyi, Z.L. Nagy, A simple proof of the Zeilberger–Bressoud \(q\)-Dyson theorem. Proc. Am. Math. Soc. 142, 3007–3011 (2014). arXiv:1211.6484
G. Károlyi, Z.L. Nagy, F.V. Petrov, V. Volkov, A new approach to constant term identities and Selberg-type integrals. Adv. Math. 277, 252–282 (2015). arXiv:1312.6369
M. Lasoń, A generalization of Combinatorial Nullstellensatz. Electron. J. Comb. 17(32), 1–6 (2010)
J. Lipman, Dualizing Sheaves, Differentials and Residues on Algebraic Varieties, vol. 117, Astérisque (Société mathématique de France, Marseille, 1984)
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Supported by the Federal professorship program Grant 1.456.2016/1.4 and the Russian Foundation for Basic Research Grant 18-01-00036.
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Karasev, R. Residues and the Combinatorial Nullstellensatz. Period Math Hung 78, 157–165 (2019). https://doi.org/10.1007/s10998-018-00272-z
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DOI: https://doi.org/10.1007/s10998-018-00272-z