Related papers: A Stronger Multiple Exchange Property for M$^{\nat…
The multiple exchange property for matroid bases is generalized for valuated matroids and M$^\natural$-concave set functions. The proof is based on the Fenchel-type duality theorem in discrete convex analysis. The present result has an…
This is a survey article on the exchange properties characterizing M-natural-concave set functions and valuated matroids (M-concave set functions). The objective of this paper is to collect related results scattered in the literature and to…
The multiple exchange property for matroid bases states that for any bases $A$ and $B$ of a matroid and any subset $X\subseteq A\setminus B$, there exists a subset $Y\subseteq B\setminus A$ such that both $A-X+Y$ and $B+X-Y$ are bases. This…
We prove a new exchange property for bases of a matroid that generalizes the multiple symmetric exchange property. For every bases $B_1,\dots,B_k$ of a matroid and a subset $A_1\subset B_1$ there exist subsets $A_2\subset…
A fundamental theorem in discrete convex analysis states that a set function is M$^\natural$-concave if and only if its conjugate function is submodular. This paper gives a new proof to this fact.
The effect of replacing a basis element on the way the basis spans other elements is studied. This leads to a new characterization of binary matroids.
It was conjectured by White in 1980 that the toric ring associated to a matroid is defined by symmetric exchange relations. This conjecture was extended to discrete polymatroids by Herzog and Hibi, and they prove that the conjecture holds…
By a localization property we mean a property that preserved under localizing modules at multiplicative closed sets. The aim of this paper is to find conditions under which we can transfere a certain property of a given module to its…
The problem of covering the ground set of two matroids by a minimum number of common independent sets is notoriously hard even in very restricted settings, i.e.\ when the goal is to decide if two common independent sets suffice or not.…
In this paper we analyse financial implications of exchangeability and similar properties of finite dimensional random vectors. We show how these properties are reflected in prices of some basket options in view of the well-known put-call…
We provide evidence for five long-standing, basis-exchange conjectures for matroids by proving them for the enormous class of sparse paving matroids. We also explore the role that these matroids may play in the following problem: as a…
The way circuits, relative to a basis, are affected as a result of exchanging a basis element, is studied. As consequences, it is shown that three consecutive symmetric exchanges exist for any two bases of a matroid, and that a full serial…
The increasing interest in the Mueller density-matrix-functional theory has led us to a systematic mathematical investigation of its properties. This functional is similar to the Hartree-Fock functional, but with a modified exchange term in…
We characterize inclusions of compact noncommutative convex sets with the property that every continuous affine function on the smaller set can be extended to a continuous affine function on the larger set with a uniform bound. As an…
I introduce a favor exchange model where favors are substitutable and study bilateral enforcement of cooperation. Without substitutability, the value of a relationship does not depend on the rest of the network, and in equilibrium there is…
Though the notion of exchangeability has been discussed in the causal inference literature under various guises, it has rarely taken its original meaning as a symmetry property of probability distributions. As this property is a standard…
Using GCH, we force the following: There are continuum many simple cardinal characteristics with pairwise different values.
We consider multi-item exchange markets in which agents want to receive one of their target bundles of resources. The model encompasses well-studied markets for kidney exchange, lung exchange, and multi-organ exchange. We identify a general…
The demand for pseudopotentials constructed for a given exchange-correlation (XC) functional far exceeds the supply, necessitating the use of those commonly available. The number of XC functionals currently available is in the hundreds, if…
We study properties of the Laplace transforms of non-negative additive functionals of Markov chains. We are namely interested in a multiplicative ergodicity property used in [18] to study bifurcating processes with ancestral dependence. We…