相关论文: Maximum genus of the Jenga like configurations

We study the correlated equilibrium polytope $P_G$ of a game $G$ from a combinatorial point of view. We introduce the region of full-dimensionality for this class of polytopes and prove that it is a semialgebraic set for any game. Using a…

In this paper we obtain the extended genus field of a global field. First we define the extended genus field of a global function field and we obtain, via class field theory, the description of the extended genus field of an arbitrary…

We determine the maximum number of edges that a planar graph can have as a function of its maximum degree and matching number.

In this paper, we give a lower bound for the maximum and minimum genus of a multibranched surface by the first Betti number and the minimum and maximum genus of the boundary of the neighborhood of it, respectively. As its application, we…

Generalized Tur\'an problems investigate the maximization of the number of certain structures (typically edges) under some constraints in a graph. We study a game version of these problems, the Constructor-Blocker game. We mainly focus on…

The construction of the COMBINATORIAL data for a surface with n vertices of maximal genus is a classical problem: The maximal genus g=[(n-3)(n-4)/12] was achieved in the famous ``Map Color Theorem'' by Ringel et al. (1968). We present the…

We bound the genus of a projective curve lying on a complete intersection surface in terms of its degree and the degrees of the defining equations of the surface on which it lies.

In this survey, we discuss the problem of the maximum number of points of curves of genus 1,2 and 3 over finite fields

Although several methodologies for identifying the genealogy of video game genres and showing their relationships have been proposed in existing research, there have been few attempts to visualize the genealogy of a genre in a quantitative…

In this paper we present a new Good Characterization of maximum genus of a graph which makes a common generalization of the works of Xuong, Liu, and Fu et al. Based on this, we find a new polynomially bounded algorithm to find the maximum…

The number of Nash equilibria of the mixed extension of a generic finite game in normal form is finite and odd. This raises the question how large the number can be, depending on the number of players and the numbers of their pure…

We propose the further study of the rate of growth of the number of contiguous buildings which may be made from n LEGO blocks of the same size and color. Specializing to blocks of dimension 2x4 we give upper and lower bounds, and speculate…

In this paper, we investigate the probability of the expression of genes that control the size of beetles under competitive relationships. We use the mean field game (MFG) theory in multiple populations to characterize the different…

We compute a parametric description of the totally mixed Nash equilibria of a generic game in normal form with pre-fixed structure. Using this representation, we show conditions under which a game has the maximum possible number of this…

For line bundles on arithmetic varieties we construct height functions using arithmetic intersection theory. In the case of an arithmetic surface, generically of genus g, for line bundles of degree g equivalence is shown to the height on…

We prove the existence of a genus-zero complete maximal map with a prescribed singularity set and an arbitrary number of simple and complete ends. We also discuss the conditions under which this maximal map can be made into a complete…

We determine the zeta functions of trinomial curves in terms of Gauss sums and Jacobi sums, and we obtain an explicit formula of the genus of a trinomial curve over a finite field, then we study the conditions for a trinomial curve to be a…

We consider a randomized algorithm for the unique games problem, using independent multinomial probabilities to assign labels to the vertices of a graph. The expected value of the solution obtained by the algorithm is expressed as a…

Let $L$ be a prime alternating link with $n$ crossings. We show that for each fixed $g$, the number of genus $g$ incompressible surfaces in the complement of $L$ is bounded by a polynomial in $n$. Previous bounds were exponential in $n$.

Using a game characterization of distributivity, we show that base matrices for $\mathcal{P}(\omega)/\text{fin}$ of regular height larger than $\mathfrak{h}$ necessarily have maximal branches which are not cofinal.