Results 51 to 60 of about 1,715 (93)
The canonical representation of the Drinfeld curve
Mathematische Nachrichten, Volume 297, Issue 11, Page 4115-4120, November 2024.Abstract If C$C$ is a smooth projective curve over an algebraically closed field F$\mathbb {F}$ and G$G$ is a group of automorphisms of C$C$, the canonical representation of C$C$ is given by the induced F$\mathbb {F}$‐linear action of G$G$ on the vector space H0C,ΩC$H^0\left(C,\Omega _C\right)$ of holomorphic differentials on C$C$.
Lucas Laurent, Bernhard Köck
wiley +1 more source
Polynomial‐exponential equations — Some new cases of solvability
Proceedings of the London Mathematical Society, Volume 129, Issue 4, October 2024.Abstract Recently, Brownawell and the second author proved a ‘non‐degenerate’ case of the (unproved) ‘Zilber Nullstellensatz’ in connexion with ‘Strong Exponential Closure’. Here, we treat some significant new cases. In particular, these settle completely the problem of solving polynomial‐exponential equations in two complex variables.
Vincenzo Mantova, David Masser
wiley +1 more source
Expressing Combinatorial Problems by Systems of Polynomial Equations and Hilbert's Nullstellensatz [PDF]
Combinatorics, Probability and Computing, 2009 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-colourable, Hamiltonian, etc.) if and only if a related system of polynomial equations has a solution.For an infeasible polynomial system, the (complex) Hilbert ...
De Loera, J. A. +3 more
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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
wiley +1 more source
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
Total weight choosability in Hypergraphs [PDF]
, 2013 A total weighting of the vertices and edges of a hypergraph is called vertex-coloring if the total weights of the vertices yield a proper coloring of the graph, i.e., every edge contains at least two vertices with different weighted degrees. In this note
Pfender, Florian
core
Gr\"obner Bases and Nullstellens\"atze for Graph-Coloring Ideals [PDF]
, 2014 We revisit a well-known family of polynomial ideals encoding the problem of graph-$k$-colorability. Our paper describes how the inherent combinatorial structure of the ideals implies several interesting algebraic properties.
De Loera, Jesús A. +7 more
core
Border bases and order ideals: a polyhedral characterization
, 2015 Border bases arise as a canonical generalization of Gr\"obner bases. We provide a polyhedral characterization of all order ideals (and hence border bases) that are supported by a zero-dimensional ideal: order ideals that support a border basis correspond
Braun, Gábor, Pokutta, Sebastian
core +1 more source
Recognizing Graph Theoretic Properties with Polynomial Ideals [PDF]
, 2010 Many hard combinatorial problems can be modeled by a system of polynomial equations. N. Alon coined the term polynomial method to describe the use of nonlinear polynomials when solving combinatorial problems. We continue the exploration of the polynomial
De Loera, J. A. +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\
openaire +2 more sources