Results 41 to 50 of about 107 (87)
Analytic Nullstellensätze and the model theory of valued fields
Mathematische Nachrichten, Volume 297, Issue 8, Page 2873-2917, August 2024.Abstract We present a uniform framework for establishing Nullstellensätze for power series rings using quantifier elimination results for valued fields. As an application, we obtain Nullstellensätze for p$p$‐adic power series (both formal and convergent) analogous to Rückert's complex and Risler's real Nullstellensatz, as well as a p$p$‐adic analytic ...
Matthias Aschenbrenner, Ahmed Srhir
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Blocking sets, minimal codes and trifferent codes
Journal of the London Mathematical Society, Volume 109, Issue 6, June 2024.Abstract We prove new upper bounds on the smallest size of affine blocking sets, that is, sets of points in a finite affine space that intersect every affine subspace of a fixed codimension. We show an equivalence between affine blocking sets with respect to codimension‐2 subspaces that are generated by taking a union of lines through the origin, and ...
Anurag Bishnoi +3 more
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Combinatorial Nullstellensatz Modulo Prime Powers and the Parity Argument [PDF]
The Electronic Journal of Combinatorics, 2014 We present new generalizations of Olson's theorem and of a consequence of Alon's Combinatorial Nullstellensatz. These enable us to extend some of their combinatorial applications with conditions modulo primes to conditions modulo prime powers. We analyze computational search problems corresponding to these kinds of combinatorial questions and we prove ...
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Combinatorial Nullstellensatz approach to polynomial expansion
Acta Arithmetica, 2014 Applying techniques similar to Combinatorial Nullstellensatz we prove a lower estimate of $|f(A,B)|$ for finite subsets $A$, $B$ of a field, and polynomial $f(x,y)$ of the form $f(x,y)=g(x)+yh(x)$, where degree of $g$ is greater then degree of $h$.
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Combinatorial Nullstellensatz Techniques
CoRRWe 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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Computing infeasibility certificates for combinatorial problems through Hilbert’s Nullstellensatz
Journal of Symbolic Computation, 2011 Systems of polynomial equations over a field can yield compact models of difficult combinatorial problems and they can be used to prove combinatorial results. In particular, existence of the solutions of the systems means that the combinatorial objects have the properties captured by the systems.
Jesús A. De Loera +3 more
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Quantitative Combinatorial Nullstellensatz
, 2012 The main result of this paper is a coefficient formula that sharpens and generalizes Alon and Tarsi's Combinatorial Nullstellensatz, which provides some information about the polynomial map $P|_{\X_1\times...\times\X_n}$ when only incomplete information about the polynomial $P(X_1,...c,X_n)$ is given. In a very general working frame, the grid points $x\
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Algebra, Geometry and Topology of ERK Kinetics. [PDF]
Bull Math Biol, 2022 Marsh L +3 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.
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