Related papers: Combinatorial Characterizations of K-matrices

We introduce and study a $K$-theory of twisted bundles for associative algebras $A(\mathfrak g)$ of formal series with an infinite-Lie algebra coefficients over arbitrary compact topological spaces. Fibers of such bundles are given by…

This article presents a validation of a recently proposed strongly polynomial-time algorithm for the general linear programming problem. The proposed algorithm is an implicit reduction procedure that combines primal and dual linear…

Discrete combinatorial optimization has a central role in many scientific disciplines, however, for hard problems we lack linear time algorithms that would allow us to solve very large instances. Moreover, it is still unclear what are the…

We introduce combinatorial objects named matricubes that provide a generalization of the theory of matroids. As matroids provide a combinatorial axiomatization of hyperplane arrangements, matricubes provide a combinatorial axiomatization of…

Heckman and Opdam introduced a non-symmetric analogue of Jack polynomials using Cherednik operators. In this paper, we derive a simple recursion formula for these polynomials and formulas relating the symmetric Jack polynomials with the…

The K-theoretic quiver component formula expresses the K-polynomial of a type A quiver locus as an alternating sum of products of double Grothendieck polynomials. This formula was conjectured by A. Buch and R. Rim\'anyi and later proved by…

We introduce the convex combinatorial optimization problem, a far reaching generalization of the standard linear combinatorial optimization problem. We show that it is strongly polynomial time solvable over any edge-guaranteed family, and…

We present two hypermatrix formulations of the Cayley Hamilton theorem. One of the proposed formulation naturally extends to hypermatrices the combinatorial interpretations of the classical Cayley Hamilton theorem. We conclude by discussing…

We consider the algebraic K-theory of a truncated polynomial algebra in several commuting variables, K(k[x_1, ..., x_n]/(x_1^a_1, ..., x_n^a_n)). This naturally leads to a new generalization of the big Witt vectors. If k is a perfect field…

The modeling of coupled-channel effects has become increasingly important due to the availability of highly precise data for a large variety of hadronic (re)scattering processes. The K-matrix is a powerful, yet comparatively simple, method…

This paper considers three separate matrices associated to graphs and (each dimension of) cell complexes. It relates all the coefficients of their respective characteristic polynomials to the geometric and combinatorial enumeration of three…

We apply the Cartan-Kahler theorem for the k-Dirac operator studied in Clifford analysis and to the parabolic version of this operator. We show that for k = 2 the tableaux of the first prolongations of these two operators are involutive.…

Let $K$ be a $k$-dimensional simplicial complex having $n$ faces of dimension $k$, and $M$ a closed $(k-1)$-connected PL $2k$-dimensional manifold. We prove that for $k\ge3$ odd $K$ embeds into $M$ if and only if there are $\bullet$ a…

We formulate some conjectures about the K-theory of symplectic manifolds and their Fukaya categories, and prove some of them in very special cases.

In this article we give a computational study of combinatorics of the discriminantal arrangements. The discriminantal arrangements are parametrized by two positive integers n and k such that n>k. The intersection lattice of the…

This article describes certain ratios that attend pairs of complementary Gauss-Jordan pivotings transforming skew-symmetric matrices. Our interest in those ratios was motivated by a need to prove a crucial Claim stated in a recently…

The paper focuses on some versions of connected dominating set problems: basic problems and multicriteria problems. A literature survey on basic problem formulations and solving approaches is presented. The basic connected dominating set…

Matroids are a fundamental object of study in combinatorial optimization. Three closely related and important problems involving matroids are maximizing the size of the union of $k$ independent sets (that is, $k$-fold matroid union),…

We describe an explicit chain map from the standard resolution to the minimal resolution for the finite cyclic group Z_k of order k. We then demonstrate how such a chain map induces a "Z_k-combinatorial Stokes theorem", which in turn…

Here we consider the image of the principal minor map of symmetric matrices over an arbitrary unique factorization domain $R$. By exploiting a connection with symmetric determinantal representations, we characterize the image of the…