Results 21 to 30 of about 507 (44)

On the rank functions of $\mathcal{H}$-matroids

, 2016
The notion of $\mathcal{H}$-matroids was introduced by U. Faigle and S. Fujishige in 2009 as a general model for matroids and the greedy algorithm. They gave a characterization of $\mathcal{H}$-matroids by the greedy algorithm.
Sano, Yoshio
core   +2 more sources

Odd circuits in dense binary matroids [PDF]

, 2014
We show that, for each real number $\alpha > 0$ and odd integer $k\ge 5$ there is an integer $c$ such that, if $M$ is a simple binary matroid with $|M| \ge \alpha 2^{r(M)}$ and with no $k$-element circuit, then $M$ has critical number at most $c$.
Geelen, Jim, Nelson, Peter
core  

Orthogonal matroids over tracts

Forum of Mathematics, Sigma
We generalize Baker–Bowler’s theory of matroids over tracts to orthogonal matroids, define orthogonal matroids with coefficients in tracts in terms of Wick functions, orthogonal signatures, circuit sets and orthogonal vector sets, and establish basic ...
Tong Jin, Donggyu Kim
doaj   +1 more source

Computing the Tutte Polynomial of a Matroid from its Lattice of Cyclic Flats [PDF]

, 2014
We show how the Tutte polynomial of a matroid $M$ can be computed from its condensed configuration, which is a statistic of its lattice of cyclic flats.
Eberhardt, Jens Niklas
core   +1 more source

The critical number of dense triangle-free binary matroids

, 2016
We show that, for each real number $\epsilon > 0$ there is an integer $c$ such that, if $M$ is a simple triangle-free binary matroid with $|M| \ge (\tfrac{1}{4} + \epsilon) 2^{r(M)}$, then $M$ has critical number at most $c$.
Geelen, Jim, Nelson, Peter
core   +1 more source

On the structure of spikes II

AKCE International Journal of Graphs and Combinatorics
The class spike is an important class of 3-connected matroids. For an integer [Formula: see text], each matroid that is obtained by relaxing one of the circuit-hyperplanes of an r-spike (spike with rank r) is isomorphic to another r-spike and repeating ...
Vahid Ghorbani, Ghodratollah Azdi, Habib Azanchiler   +2 more
doaj   +1 more source

Potentials of a Frobenius like structure

, 2017
This paper proves the existence of potentials of the first and second kind of a Frobenius like structure in a frame which encompasses families of arrangements. The frame uses the notion of matroids.
Hertling, Claus, Varchenko, Alexander
core   +1 more source

Elementary lift and single element coextension of a binary gammoid

AKCE International Journal of Graphs and Combinatorics
It is known that every binary elementary lift of a binary matroid is a matroid obtained by applying the splitting operation on that matroid. An elementary lift of a binary gammoid need not be a binary gammoid.
Shital Dilip Solanki, Ganesh Mundhe, S. B. Dhotre   +2 more
doaj   +1 more source

Book inequalities

, 2014
Information theoretical inequalities have strong ties with polymatroids and their representability. A polymatroid is entropic if its rank function is given by the Shannon entropy of the subsets of some discrete random variables.
Csirmaz, Laszlo
core   +1 more source

Around matrix-tree theorem

, 2006
Generalizing the classical matrix-tree theorem we provide a formula counting subgraphs of a given graph with a fixed 2-core. We use this generalization to obtain an analog of the matrix-tree theorem for the root system $D_n$ (the classical theorem ...
Burman, Yurii, Shapiro, Boris
core   +3 more sources