Results 51 to 60 of about 1,707 (110)
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
wiley +1 more source
Limitations of Algebraic Approaches to Graph Isomorphism Testing
, 2015 We investigate the power of graph isomorphism algorithms based on algebraic reasoning techniques like Gr\"obner basis computation. The idea of these algorithms is to encode two graphs into a system of equations that are satisfiable if and only if if the ...
A Atserias +10 more
core +1 more source
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.
De Loera, Jesús A. +3 more
openaire +2 more sources
4-choosability of planar graphs with 4-cycles far apart via the Combinatorial Nullstellensatz
Discrete Mathematics, 2023 By a well-known theorem of Thomassen and a planar graph depicted by Voigt, we know that every planar graph is $5$-choosable, and the bound is tight. In 1999, Lam, Xu and Liu reduced $5$ to $4$ on $C_4$-free planar graphs. In the paper, by applying the famous Combinatorial Nullstellensatz, we design an effective algorithm to deal with list coloring ...
Fan Yang, Yue Wang, Jian-Liang Wu
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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\
openaire +2 more sources
A Combinatorial Proof of the Effective Nullstellensatz
Journal of Symbolic Computation, 1993 The degree bound in the effective Nullstellensatz is obtained using combinatorial methods, namely counting arguments for the ideal \(I\).
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A polyhedral approach to computing border bases [PDF]
, 2010 Border bases can be considered to be the natural extension of Gr\"obner bases that have several advantages. Unfortunately, to date the classical border basis algorithm relies on (degree-compatible) term orderings and implicitly on reduced Gr\"obner bases.
Braun, Gábor, Pokutta, Sebastian
core
Motivated exposition of combinatorial Nullstellensatz
9 pages; in ...
Lozhkin, M., Skopenkov, A.
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The Generalized Combinatorial Lason-Alon-Zippel-Schwartz Nullstellensatz Lemma
, 2023 19 pages, 3 ...
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Algebra, Geometry and Topology of ERK Kinetics. [PDF]
Bull Math Biol, 2022 Marsh L +3 more
europepmc +1 more source