Related papers: A Complementarity Partition Theorem for Multifold …

Inspired by G. Frieden's recent work on the geometric R-matrix for affine type A crystal associated with rectangular shaped Young tableaux, we propose a method to construct a novel family of discrete integrable systems which can be regarded…

We introduce the problem of partitioning 2D regions (usually convex regions) into mutually congruent pieces ('tiles').

Let $\mathbb{K}$ be a finite commutative ring, and let $\mathbb{L}$ be a commutative $\mathbb{K}$-algebra. Let $A$ and $B$ be two $n \times n$-matrices over $\mathbb{L}$ that have the same characteristic polynomial. The main result of this…

This paper presents a canonical duality theory for solving a general nonconvex constrained optimization problem within a unified framework to cover Lagrange multiplier method and KKT theory. It is proved that if both target function and…

An antinorm is a concave analogue of a norm. In contrast to norms, antinorms are not defined on the entire space $R^d$ but on a cone $K\subset R^d$. They are applied in the matrix analysis, optimal control, and dynamical systems. Their…

We present a semiclassical trace formula for the canonical partition function of arbitrary one-dimensional systems. The approximation is obtained via the stationary exponent method applied to the phase-space integration of the density…

We show that the dimer model on a bipartite graph on a torus gives rise to a quantum integrable system of special type - a cluster integrable system. The phase space of the classical system contains, as an open dense subset, the moduli…

A seminal theorem of Tverberg states that any set of $T(r,d)=(r-1)(d+1)+1$ points in $\mathbb{R}^d$ can be partitioned into $r$ subsets whose convex hulls have non-empty $r$-fold intersection. Almost any collection of fewer points in…

In this paper, we introduce polynomial time algorithms that generate random $k$-noncrossing partitions and 2-regular, $k$-noncrossing partitions with uniform probability. A $k$-noncrossing partition does not contain any $k$ mutually…

Menger's theorem says that, for $k\ge0$, if $S, T$ are sets of vertices in a graph $G$, then either there are $k + 1$ vertex-disjoint paths between $S$ and $T$, or there is a set X of at most $k$ vertices such that every $S$-$T$ path passes…

Motivated by a connection with the factorization of multivariate polynomials, we study integral convex polytopes and their integral decompositions in the sense of the Minkowski sum. We first show that deciding decomposability of integral…

Let $M$ be a symplectic toric manifold acted on by a torus $\mathbb{T}$. In this work we exhibit an explicit basis for the equivariant K-theory ring $\mathcal{K}_{\mathbb{T}}(M)$ which is canonically associated to a generic component of the…

In this paper, we give a conjecture, which generalises Euler's partition theorem involving odd parts and different parts for all moduli. We prove this conjecture for two family partitions. We give $q$-difference equations for the related…

The notion of composite system made up of distinguishable parties is investigated in the context of arbitrary convex spaces.

We consider the problem of determining the closure of a quadratic module M in a commutative R-algebra with respect to the finest locally convex topology. This is of interest in deciding when the moment problem is solvable and in analyzing…

This paper presents a canonical duality approach for solving a general topology optimization problem of nonlinear elastic structures. By using finite element method, this most challenging problem can be formulated as a mixed integer…

A Cartesian decomposition of a coherent configuration $\cal X$ is defined as a special set of its parabolics that form a Cartesian decomposition of the underlying set. It turns out that every tensor decomposition of $\cal X$ comes from a…

Coherent spaces spanned by a finite number of coherent states, are introduced. Their coherence properties are studied, using the Dirac contour representation. It is shown that the corresponding projectors resolve the identity, and that they…

Piecewise linear vector optimization problems in a locally convex Hausdorff topological vector spaces setting are considered in this paper. The efficient solution set of these problems are shown to be the unions of finitely many semi-closed…

A graph has a perfect partition if all its perfect matchings can be partitioned so that each part is a 1-factorization of the graph. Let $L_{rm, r}=K_{rm,rm}-mK_{r,r}$. We first give a formula to count the number of perfect matchings of…