Results 61 to 70 of about 1,707 (110)

On the Polynomial Parity Argument Complexity of the Combinatorial Nullstellensatz

, 2017
26 ...
Belovs, Aleksandrs, Ivanyos, Gábor, Qiao, Youming, Santha, Miklos, Yang, Siyi   +4 more
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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.
europepmc   +1 more source

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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Neighbour sum distinguishing total colourings via the Combinatorial Nullstellensatz

Discrete Applied Mathematics, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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Expressing Combinatorial Optimization Problems by Systems of Polynomial Equations and the Nullstellensatz

, 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., Lee, J., Margulies, S., Onn, S.   +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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Applications of the Combinatorial Nullstellensatz on bipartite graphs.

, 2015
APPLICATIONS OF THE COMBINATORIAL NULLSTELLENSATZ ON BIPARTITE GRAPHS Timothy M. Brauch May 9,2009 The Combinatorial Nullstellensatz can be used to solve certain problems in combinatorics. However, one of the major complications in using the Combinatorial Nullstellensatz is ensuring that there exists a nonzero monomial.
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Combinatorial Nullstellensatz and Turán numbers of complete r-partite r-uniform hypergraphs

Discrete Mathematics
3 ...
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