Results 31 to 40 of about 507 (44)
Connectivity Functions and Polymatroids
, 2016 A {\em connectivity function on} a set $E$ is a function $\lambda:2^E\rightarrow \mathbb R$ such that $\lambda(\emptyset)=0$, that $\lambda(X)=\lambda(E-X)$ for all $X\subseteq E$ and that $\lambda(X\cap Y)+\lambda(X\cup Y)\leq \lambda(X)+\lambda(Y)$ for
Jowett, Susan +2 more
core +1 more source
A Note on the Sticky Matroid Conjecture
, 2009 A matroid is sticky if any two of its extensions by disjoint sets can be glued together along the common restriction (that is, they have an amalgam). The sticky matroid conjecture asserts that a matroid is sticky if and only if it is modular.
Bonin, Joseph E.
core
On minor-closed classes of matroids with exponential growth rate [PDF]
, 2011 Let $\cM$ be a minor-closed class of matroids that does not contain arbitrarily long lines. The growth rate function, $h:\bN\rightarrow \bN$ of $\cM$ is given by $$h(n) = \max(|M|\, : \, M\in \cM, simple, rank-$n$).$$ The Growth Rate Theorem shows that ...
Geelen, Jim, Nelson, Peter
core
Tropical Carathéodory with Matroids. [PDF]
Discrete Comput Geom, 2023 Loho G, Sanyal R.
europepmc +1 more source
Rank three matroids are Rayleigh
, 2004 A Rayleigh matroid is one which satisfies a set of inequalities analogous to the Rayleigh monotonicity property of linear resistive electrical networks. We show that every matroid of rank three satisfies these inequalities.Comment: 11 pages, 3 figures, 3
Wagner, David G.
core +2 more sources
Semi-streaming algorithms for submodular matroid intersection. [PDF]
Math Program, 2023 Garg P, Jordan L, Svensson O.
europepmc +1 more source
Complete graphs: the space of simplicial cones, and their path tree representation
, 2017 Let $G$ be a complete graph with $n+1$ vertices. In a recent paper of the authors, it is shown that the path trees of the graph play a special role in the structure of the truncated powers and partition functions that are associated with the graph ...
Ron, Amos, Shengnan, Wang
core
Characterizations of transversal and fundamental transversal matroids
, 2010 A result of Mason, as refined by Ingleton, characterizes transversal matroids as the matroids that satisfy a set of inequalities that relate the ranks of intersections and unions of nonempty sets of cyclic flats.
Bonin, Joseph E. +2 more
core
Sequentially Cohen-Macaulay matroidal ideals
, 2019 Let $R=K[x_1,...,x_n]$ be the polynomial ring in $n$ variables over a field $K$ and let $J$ be a matroidal ideal of degree $d$ in $R$. In this paper, we study the class of sequentially Cohen-Macaulay matroidal ideals.
Jafari, Madineh +2 more
core
Roadblocked monotonic paths and the enumeration of coalescent histories for non-matching caterpillar gene trees and species trees. [PDF]
Adv Appl Math, 2020 Himwich ZM, Rosenberg NA.
europepmc +1 more source