相关论文: On the inverse Kostka matrix
We give several equivalent combinatorial descriptions of the space of states for the box-ball systems, and connect certain partition functions for these models with the q-weight multiplicities of the tensor product of the fundamental…
We present here necessary and sufficient conditions for the invertibility of circulant and symmetric matrices that depend on three parameters and moreover, we explicitly compute the inverse. The techniques we use are related with the…
We study a nonlinear decomposition of a positive definite matrix into two components: the inverse of another positive definite matrix and a symmetric matrix constrained to lie in a prescribed linear subspace. Equivalently, the inverse…
We propose the representation principle to study physical systems with a given symmetry. In the context of symmetry enriched topological orders, we give the appropriate representation category, the category of SET orders, which include SPT…
In this paper, we derive an inverse result for bivariate Kantorovich type sampling series for the space of all continuous functions with upto second order partial derivatives are continuous and bounded on $R^2.$ Further, we prove the rate…
We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…
This note considers linear recurrences (also called linear difference equations) in unknowns indexed by the integers. We characterize a unique \emph{reduced} linear recurrence with the same solutions as a given linear recurrence, and…
We study the problem of determining a matrix whose $k$th multiplicative compound is a prescribed matrix~$M$. The cardinality of the set of matrices whose $k$th multiplicative compound equals~$M$ is characterized in terms of $\rank(M)$. On…
A construction of the noncommutative-geometric counterparts of classical classifying spaces is presented, for general compact matrix quantum structure groups. A quantum analogue of the classical concept of the classifying map is introduced…
We introduce combinatorial multivector fields, associate with them multivalued dynamics and study their topological features. Our combinatorial multivector fields generalize combinatorial vector fields of Forman. We define isolated…
We generalize Monge property of real matrices for interval matrices. We define two classes of interval matrices with Monge property - in a strong and in a weak sense. We study fundamental properties of both classes. We show several…
Boolean-type algebra (BTA) is investigated. A BTA is decomposed into Boolean-type lattice (BTL) and a complementation algebra (CA). When the object set is finite, the matrix expressions of BTL and CA (and then BTA) are presented. The…
Representation theory of the symmetric group $\mathfrak{S}_n$ has a very distinctive combinatorial flavor. The conjugacy classes as well as the irreducible characters are indexed by integer partitions $\lambda \vdash n$. We introduce class…
We introduce a novel approach that employs techniques from noncommutative Poisson geometry to comprehend the algebra of invariants of two $n\times n$ matrices. We entirely solve the open problem of computing the algebra of invariants of two…
In this article, we consider birational equivalence of exponential matrices. In characteristic zero, we give a birational classification of exponential matrices of size $n$-by-$n$ $(n \geq 2)$, which consists of two types. And in positive…
Given standard angular momentum and boost matrices, the commutation rules for vector and momentum matrices are solved. The resulting matrix components are displayed as detailed functions of spin with factors such as the square root of…
In this paper, we have constructed the higher order k-bonacci matrices and studied some of their basic properties. We have also shown that these matrices satisfying some new and interesting relations in k-bonacci recurrence. This is the…
We apply the nested algebraic Bethe ansatz to a model of one-dimensional two-component Bose gas with delta-function repulsive interaction. Using a lattice approximation of the L-operator we find Bethe vectors of the model in the continuous…
We combinatorially prove a new recurrence between the Tutte polynomials of graphs obtained by contraction of the complete graphs $K_{n}$%. This generalizes, to two variables, a relation previously obtained by the author between the…
This is a survey of recent developments in combinatorics. The goal is to give a big picture of its many interactions with other areas of mathematics, such as: group theory, representation theory, commutative algebra, geometry (including…