Related papers: Higher matrix-tree theorems

We introduce generalized multipliers for left-invertible analytic operators. We show that they form a Banach algebra and characterize the commutant of such operators in its terms. In the special case, we describe the commutant of balanced…

We unite elements of category theory, K-theory, and geometric group theory, by defining a class of groups called $k$-cube groups, which act freely and transitively on the product of $k$ trees, for arbitrary $k$. The quotient of this action…

On base of differential biquaternions algebra and generalized functions theory the biquaternionic wave equation is considered under vector representation of its structural coefficient. Its generalized solutions are constructed, which…

Connections between set-theoretic Yang-Baxter and reflection equations and quantum integrable systems are investigated. We show that set-theoretic $R$-matrices are expressed as twists of known solutions. We then focus on reflection and…

We prove the hard Lefschetz theorem and the Hodge-Riemann relations for a commutative ring associated to an arbitrary matroid M. We use the Hodge-Riemann relations to resolve a conjecture of Heron, Rota, and Welsh that postulates the…

We present a determinantal formula for the number of spanning trees of a complete multipartite graph containing a given spanning forest $F$. Our approach relies on the Generalized Matrix Determinant Lemma and Jacobi's formula for the…

Herein, the theory of Bergman kernel is developed to the weighted case. A general form of weighted Bergman reproducing kernel is obtained, by which we can calculate concrete Bergman kernel functions for specific weights and domains.

We decompose the weighted subobject commutator of M. Gran, G. Janelidze and A. Ursini as a join of a binary and a ternary commutator.

We prove an explicit formula for a projection of singular vectors in the Verma module over a rank 2 Kac-Moody Lie algebra onto the universal enveloping algebra of the Heisenberg Lie algebra and of $sl_{2}$ (Theorem 3). The formula is…

We compute the R-matrix which intertwines two dimensional evaluation representations with Drinfeld comultiplication for U_q(\widehat{sl}_2). This R-matrix contains terms proportional to the delta-function. We construct the algebra A(R)…

For a large class of C*-algebras $A$, we calculate the $K$-theory of reduced crossed products $A^{\otimes G}\rtimes_rG$ of Bernoulli shifts by groups satisfying the Baum--Connes conjecture. In particular, we give explicit formulas for…

Gerstenhaber showed in 1961 that any commuting pair of n x n matrices over a field k generates a k-algebra A of k-dimension \leq n. A well-known example shows that the corresponding statement for 4 matrices is false. The question for 3…

Steinberg showed that when a finite reflection group acts on a real or complex vector space of finite dimension, the Jacobian determinant of a set of basic invariants factors into linear forms which define the reflecting hyperplanes. This…

We use the properties of Hermite and Kamp\'e de F\'eriet polynomials to get closed forms for the repeated derivatives of functions whose argument is a quadratic or higher-order polynomial. The results we obtain are extended to product of…

Motivated by the theory of weighted shifts on directed trees and its multivariable counterpart, we address the question of identifying commutant and reflexivity of the multiplication $d$-tuple $\mathscr M_z$ on a reproducing kernel Hilbert…

We give a universal construction of families of Hopf $P$-algebras for any Hopf operad $P$. As a special case, we recover the Connes-Kreimer Hopf algebra of rooted trees.

We obtain an array of consistency results concerning trees and stationary reflection at double successors of regular cardinals $\kappa$, updating some classical constructions in the process. This includes models of…

Matroids generalize the familiar notion of linear dependence from linear algebra. Following a brief discussion of founding work in computability and matroids, we use the techniques of reverse mathematics to determine the logical strength of…

We study highest weight vectors for symmetric and alternating spaces of tensors, whose dimensions are given by generalized Kronecker coefficients. We describe the algebraic relations for classical constructions of corresponding spanning…

The Markov Chain Tree Theorem is extended to the max algebra and possible applications to ranking problems are discussed.