Results 31 to 40 of about 107 (87)

The Alon-Tarsi number of cupolarotundas and gyroelongated rotunda

Electronic Journal of Graph Theory and Applications
The Alon-Tarsi number of a graph G is the smallest k so that there exists an orientation D of G with max outdegree k - 1 satisfying the number of even Eulerian subgraphs different from the number of odd Eulerian subgraphs.
Zhiguo Li, Yujia Gai, Zeling Shao
doaj   +1 more source

On the natural nullcones of the symplectic and general linear groups

Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.
Abstract Consider a group acting on a polynomial ring S$S$ over a field K$\mathbb {K}$ by degree‐preserving K$\mathbb {K}$‐algebra automorphisms. Several key properties of the invariant ring can be deduced by studying the nullcone of the action, that is, the vanishing locus of all nonconstant homogeneous invariant polynomials.
Vaibhav Pandey, Yevgeniya Tarasova, Uli Walther   +2 more
wiley   +1 more source

New Exact Solutions of Some Nonlinear Systems of Partial Differential Equations Using the First Integral Method

Abstract and Applied Analysis, Volume 2013, Issue 1, 2013., 2013
The first integral method introduced by Feng is adopted for solving some important nonlinear systems of partial differential equations, including classical Drinfel′d‐Sokolov‐Wilson system (DSWE), (2 + 1)‐dimensional Davey‐Stewartson system, and generalized Hirota‐Satsuma coupled KdV system. This method provides polynomial first integrals for autonomous
Shoukry Ibrahim Atia El-Ganaini, Elena Litsyn   +1 more
wiley   +1 more source

On some matrix counting problems

Journal of the London Mathematical Society, Volume 110, Issue 6, December 2024.
Abstract We estimate the frequency of singular matrices and of matrices of a given rank whose entries are parametrised by arbitrary polynomials over the integers and modulo a prime p$p$. In particular, in the integer case, we improve a recent bound of V. Blomer and J. Li (2022).
Ali Mohammadi, Alina Ostafe, Igor E. Shparlinski   +2 more
wiley   +1 more source

On linear algebraic semigroups III

International Journal of Mathematics and Mathematical Sciences, Volume 4, Issue 4, Page 667-690, 1981., 1981
Using some results on linear algebraic groups, we show that every connected linear algebraic semigroup S contains a closed, connected diagonalizable subsemigroup T with zero such that E(T) intersects each regular J‐class of S. It is also shown that the lattice (E(T), ≤) is isomorphic to the lattice of faces of a rational polytope in some ℝn.
Mohan S. Putcha
wiley   +1 more source

A short proof of Combinatorial Nullstellensatz

Am. Math. Mon., 2009
In this note we give a short, direct proof of the well known Combinatorial Nullstellensatz.
openaire   +2 more sources

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 ...
Jesús A. De Loera, Jon Lee 0001, Susan Margulies, Shmuel Onn   +3 more
openaire   +2 more sources

Neighbor Sum Distinguishing Total Choice Number of IC-Planar Graphs Without 4-Cycles

Mathematics
A neighbor sum distinguishing (NSD) total coloring of a graph G is a mapping ϕ:T(G)=V(G)∪E(G)→{1,2,⋯,k} such that any two adjacent or incident elements in T(G) receive different colors, and the sum of the colors of all incident edges of u and the color ...
Meili Ye, Donghan Zhang
doaj   +1 more source

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