Results 61 to 70 of about 1,715 (93)
Motivated exposition of combinatorial Nullstellensatz
9 pages; in ...
Lozhkin, M., Skopenkov, A.
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Algebra, Geometry and Topology of ERK Kinetics. [PDF]
Bull Math Biol, 2022 Marsh L +3 more
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The Generalized Combinatorial Lason-Alon-Zippel-Schwartz Nullstellensatz Lemma
, 2023 19 pages, 3 ...
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Topological Noetherianity of polynomial functors II: base rings with Noetherian spectrum. [PDF]
Math Ann, 2023 Bik A, Danelon A, Draisma J.
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On the Polynomial Parity Argument Complexity of the Combinatorial Nullstellensatz
, 2017 26 ...
Belovs, Aleksandrs +4 more
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Combinatorial Nullstellensatz Techniques
We present different techniques for applying Combinatorial Nullstellensatz to polynomials over finite fields. For examples, we generalize theorems from Noga Alon's paper on the subject, and present a few of our own.
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Proof of the Combinatorial Nullstellensatz over Integral Domains, in the Spirit of Kouba [PDF]
The Electronic Journal of Combinatorics, 2010 It is shown that by eliminating duality theory of vector spaces from a recent proof of Kouba [A duality based proof of the Combinatorial Nullstellensatz, Electron. J. Combin. 16 (2009), #N9] one obtains a direct proof of the nonvanishing-version of Alon's Combinatorial Nullstellensatz for polynomials over an arbitrary integral domain.
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Computational Aspects of the Combinatorial Nullstellensatz Method
, 2014 We discuss here some computational aspects of the Combinatorial Nullstellensatz argument. Our main result shows that the order of magnitude of the symmetry group associated with permutations of the variables in algebraic constraints, determines the performance of algorithms naturally deduced from Alon's Combinatorial Nullstellensatz arguments.
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, 2007 Systems of polynomial equations over the complex or real numbers can be used to model combinatorial problems. In this way, a combinatorial problem is feasible (e.g. a graph is 3-colorable, hamiltonian, etc.) if and only if a related system of polynomial equations has a solution. In the first part of this paper, we construct new polynomial encodings for
De Loera, J. A. +3 more
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Combinatorial nullstellensatz and its applications
, 2019 In 1999, Noga Alon proved a theorem, which he called the Combinatorial Nullstellensatz, that gives an upper bound to the number of zeros of a multivariate polynomial. The theorem has since seen heavy use in combinatorics, and more specifically in graph theory.
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