Related papers: Connectivity Functions and Polymatroids

The present note is a strengthening of a recent paper by K. Takazawa and Y. Yokoi (A generalized-polymatroid approach to disjoint common independent sets in two matroids, Discrete Mathematics (2019)). For given two matroids on $E$, under…

A pseudo-length function defined on an arbitrary group $G = (G,\cdot,e, (\,)^{-1})$ is a map $\ell: G \to [0,+\infty)$ obeying $\ell(e)=0$, the symmetry property $\ell(x^{-1}) = \ell(x)$, and the triangle inequality $\ell(xy) \leqslant…

In this paper, the concordance of Morse functions is defined, and a necessary and sufficient condition for given two Morse functions to be concordant is presented and is compared with the cobordism criterion. Cobordism of Morse functions on…

We introduce the notion of a matroid M over a commutative ring R, assigning to every subset of the ground set an R-module according to some axioms. When R is a field, we recover matroids. When R=$\mathbb{Z}$, and when R is a DVR, we get…

This paper introduces a new automata-theoretic class of string-to-string functions with polynomial growth. Several equivalent definitions are provided: a machine model which is a restricted variant of pebble transducers, and a few inductive…

The {\it profile} of a relational structure $R$ is the function $\phi_R$ which counts for every integer $n$ the number of its $n$-element substructures up to an isomorphism. Many counting functions are profiles. Interesting examples come…

For an open set $\Om \subset \R^2$ let $\lambda(\Om)$ denote the bottom of the spectrum of the Dirichlet Laplacian acting in $L^2(\Om)$. Let $w_\Om$ be the torsion function for $\Om$, and let $\|.\|_p$ denote the $L^p$ norm. It is shown…

We adapt the "royal road" method used to simplify automatic analyticity theorems in noncommutative function theory to several complex variables. We show that certain families of functions must be real analytic if they have certain nice…

We study matroidal networks introduced by Dougherty et al. We prove the converse of the following theorem: If a network is scalar-linearly solvable over some finite field, then the network is a matroidal network associated with a…

The splitting operation on a $p$-matroid does not necessarily preserve connectivity. It is observed that there exists a single element extension of the splitting matroid which is connected. In this paper, we define the element splitting…

A super-minimally $k$-connected matroid is a $k$-connected matroid having no proper $k$-connected restriction of size at least $2k-2$. This extends the corresponding concept for graphs. For $k=2$ and $k=3$, we determine the maximum size of…

We show that the partition function of free Maxwell theory on a generic Euclidean four-manifold transforms in a non-trivial way under electric-magnetic duality. The classical part of the partition sum can be mapped onto the genus-one…

We show that for every connected analytic subvariety $V$ there is a pseudoconvex set $\Omega$ such that every bounded matrix-valued holomorphic function on $V$ extends isometrically to $\Omega$. We prove that if $V$ is two analytic disks…

In this work the interplay between matrix biorthogonal polynomials with respect to a matrix of linear functionals, the $k$-th associated matrix polynomials and the second kind matrix functions, is studied in terms of quasideterminants. A…

The classical matrix tree theorem relates the number of spanning trees of a connected graph with the product of the nonzero eigenvalues of its Laplacian matrix. The class of regular matroids generalizes that of graphical matroids, and a…

In 1993, Stanley and Stembridge conjectured that a chromatic symmetric function of any $(3+1)$-free poset is $e$-positive. Guay-Paquet reduced the conjecture to $(3+1)$- and $(2+2)$-free posets which are also called natural unit interval…

A transversal matroid whose dual is also transversal is called bi-transversal. Let $G$ be an undirected graph with vertex set $V$. In this paper, for every subset $W$ of $V$, we associate a bi-transversal matroid to the pair $(G,W)$. We…

In [S. Basu, A. Gabrielov, N. Vorobjov, Semi-monotone sets. arXiv:1004.5047v2 (2011)] we defined semi-monotone sets, as open bounded sets, definable in an o-minimal structure over the reals, and having connected intersections with all…

Let $(X, \mathscr{L}, \lambda)$ and $(Y, \mathscr{M}, \mu)$ be finite measure spaces for which there exist $A \in \mathscr{L}$ and $B \in \mathscr{M}$ with either $0 < \lambda(A) < 1 < \lambda(X)$ and $0 < \mu(B) < \mu(Y)$, or the other way…

We briefly describe what tau-functions in integrable systems are. We then define a collection of tau-functions given as matrix elements for the action of $\widehat{GL_2}$ on two-component Fermionic Fock space. These tau-functions are…