相关论文: Self-complementary plane partitions by Proctor's m…

Questions that seek to determine whether a hyperplane arrangement property, be it geometric, arithmetic or topological, is of a combinatorial nature (that is determined by the intersection lattice) are abundant in the literature. To tackle…

In the present article a new method of deriving integral representations of combinations and partitions in terms of harmonic products has been established. This method may be relevant to statistical mechanics and to number theory.

We show how to use the method of orthogonal polynomials for integrating, in the planar approximation, the partition function of one-matrix models with a potential with even or odd vertices, or any combination of them.

A quantum mechanical description of particle propagation on the discrete spacetime of a causal set is presented. The model involves a discrete path integral in which trajectories within the causal set are summed over to obtain a particle…

Given a finite collection of two-dimensional tile types, the field of study concerned with covering the plane with tiles of these types exclusively has a long history, having enjoyed great prominence in the last six to seven decades. Much…

A partitioned process theory, as defined by Coecke, Fritz, and Spekkens, is a symmetric monoidal category together with an all-object-including symmetric monoidal subcategory. We think of the morphisms of this category as processes, and the…

This paper consists of two prongs. Firstly, we prove that any Specht module labelled by a 2-separated partition is semisimple and we completely determine its decomposition as a direct sum of graded simple modules. Secondly, we apply these…

MacMahon enumerated the plane partitions in an $a \times b \times c$ box. These are in bijection to lozenge tilings of a hexagon, to certain perfect matchings, and to families of non-intersecting lattice paths. In this work we consider more…

The planar ornaments are created by repeating a base unit using a combination of four primitive geometric operations: translation, rotation, reflection, and glide reflection. According to group theory, different combinations of these four…

We study the problems of covering or partitioning a polygon $P$ (possibly with holes) using a minimum number of small pieces, where a small piece is a connected sub-polygon contained in an axis-aligned unit square. For covering, we seek to…

In this paper we give a unified treatment of two different definitions of complementarity partition of multifold conic programs introduced independently in [J. F. Bonnans and H. Ram\'irez C., Math. Program. 104 (2005), no. 2-3, Ser. B,…

The famous pancake theorem states that for every finite set $X$ in the plane, there exist two orthogonal lines that divide $X$ into four equal parts. We propose an algorithm whose running time is linear in the number of points in $X$ and…

We consider discretization of the 'geometric cover problem' in the plane: Given a set $P$ of $n$ points in the plane and a compact planar object $T_0$, find a minimum cardinality collection of planar translates of $T_0$ such that the union…

For an arrangement of $n$ pseudolines in the real projective plane let us denote by $t_i$ the number of vertices incident to $i$ lines. We obtain a linear on $t_i$ inequality similar to the Hirzebruch one, but with an elementary proof. We…

We study plane partitions satisfying condition $a_{n+1,m+1}=0$ (this condition is called "pit") and asymptotic conditions along three coordinate axes. We find the formulas for generating function of such plane partitions. Such plane…

We prove that under certain combinatorial conditions, the realization spaces of line arrangements on the complex projective plane are connected. We also give several examples of arrangements with eight, nine and ten lines which have…

We show that if the fundamental groups of the complements of two line arrangements in the complex projective plane are isomorphic to the same direct sum of free groups, then the complements of the arrangements are homotopy equivalent. For…

It is shown that the descending plane partitions of Andrews can be geometrically realized as cyclically symmetric rhombus tilings of a certain hexagon where an equilateral triangle of side length 2 has been removed from its centre. Thus,…

In this letter we calculate the exact partition function for free bosons on the plane with lacunae. First the partition function for a plane with two spherical holes is calculated by matching exactly for the infinite set of Wilson…

We study certain bijection between plane partitions and $\mathbb{N}$-matrices. As applications, we prove a Cauchy-type identity for generalized dual Grothendieck polynomials. We introduce two statistics on plane partitions, whose generating…