Results 21 to 30 of about 1,715 (93)
Abstract and Applied Analysis, Volume 2022, Issue 1, 2022., 2022 In this article, we study and investigate the analytical solutions of the space‐time nonlinear fractional modified KDV‐Zakharov‐Kuznetsov (mKDV‐ZK) equation. We have got new exact solutions of the fractional mKDV‐ZK equation by using first integral method; we found new types of hyperbolic solutions and trigonometric solutions by symbolic computation.
Mohamed A. Abdoon +3 more
wiley +1 more source
A Short Proof of Combinatorial Nullstellensatz [PDF]
The American Mathematical Monthly, 2010 In this note we give a short, direct proof of the well known Combinatorial Nullstellensatz.
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Additive List Coloring of Planar Graphs with Given Girth
Discussiones Mathematicae Graph Theory, 2020 An additive coloring of a graph G is a labeling of the vertices of G from {1, 2, . . . , k} such that two adjacent vertices have distinct sums of labels on their neighbors.
Brandt Axel +2 more
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Neighbor Sum Distinguishing Total Choosability of IC-Planar Graphs
Discussiones Mathematicae Graph Theory, 2020 Two distinct crossings are independent if the end-vertices of the crossed pair of edges are mutually different. If a graph G has a drawing in the plane such that every two crossings are independent, then we call G a plane graph with independent crossings
Song Wen-Yao +2 more
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Combinatorial Nullstellensatz [PDF]
Combinatorics, Probability and Computing, 1999 We present a general algebraic technique and discuss some of its numerous applications in combinatorial number theory, in graph theory and in combinatorics. These applications include results in additive number theory and in the study of graph colouring problems.
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A Generalization of Combinatorial Nullstellensatz [PDF]
The Electronic Journal of Combinatorics, 2010 In this note we give an extended version of Combinatorial Nullstellensatz, with weaker assumption on nonvanishing monomial. We also present an application of our result in a situation where the original theorem does not seem to work.
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Constructing integer-magic graphs via the Combinatorial Nullstellensatz
The Art of Discrete and Applied Mathematics, 2022 Summary: Let Abe a nontrivial abelian group and \(A^\ast = A \backslash \{0\}\). A graph is \(A\)-magic if there exists an edge labeling fusing elements of \(A^\ast\) which induces a constant vertex labeling of the graph. Such a labeling \(f\) is called an \(A\)-magic labeling and the constant value of the induced vertex labeling is called an \(A ...
Low, Richard M., Roberts, Dan
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Some extensions of Alon's Nullstellensatz [PDF]
, 2011 Alon's combinatorial Nullstellensatz, and in particular the resulting nonvanishing criterion is one of the most powerful algebraic tools in combinatorics, with many important applications.
Kós, Géza +2 more
core +1 more source
Computing Small Certificates of Inconsistency of Quadratic Fewnomial Systems [PDF]
, 2016 B{\'e}zout 's theorem states that dense generic systems of n multivariate quadratic equations in n variables have 2 n solutions over algebraically closed fields.
Eisenbud D. +4 more
core +5 more sources
Hilbert's nullstellensatz and an algorithm for proving combinatorial infeasibility [PDF]
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation, 2008 Systems of polynomial equations over an algebraically-closed field K can be used to concisely model many 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 over K.
De Loera, J. A. +3 more
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