Results 61 to 70 of about 14,016 (208)
The Chip Firing Game and Matroid Complexes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2001 In this paper we construct from a cographic matroid M, a pure multicomplex whose degree sequence is the h―vector of the the matroid complex of M. This result provesa conjecture of Richard Stanley [Sta96] in the particular case of cographic matroids.
Criel Merino
doaj +1 more source
Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.Abstract In 1935, Philip Hall published what is often referred to as ‘Hall's marriage theorem’ in a short paper (P. Hall, J. Lond. Math. Soc. (1) 10 (1935), no. 1, 26–30.) This paper has been very influential. I state the theorem and outline Hall's proof, together with some equivalent (or stronger) earlier results, and proceed to discuss some the many ...
Peter J. Cameron
wiley +1 more source
Multidimensional Topological Measure Spaces and Their Applications in Decision‐Making Problems
Advances in Fuzzy Systems, Volume 2026, Issue 1, 2026.This paper presents a generalized framework termed the multidimensional topological measure space (MDTMS), developed through multidimensional fuzzy sets, multidimensional topology, and an associated distance measure. The suggested framework enhances traditional fuzzy models by facilitating a more nuanced representation and examination of intricate ...
Jomal Josen +3 more
wiley +1 more source
On the number of matroids compared to the number of sparse paving matroids [PDF]
, 2014 It has been conjectured that sparse paving matroids will eventually predominate in any asymptotic enumeration of matroids, i.e. that $\lim_{n\rightarrow\infty} s_n/m_n = 1$, where $m_n$ denotes the number of matroids on $n$ elements, and $s_n$ the number
Pendavingh, Rudi, van der Pol, Jorn
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The matroid secretary problem for minor-closed classes and random matroids
, 2019 We prove that for every proper minor-closed class $M$ of matroids representable over a prime field, there exists a constant-competitive matroid secretary algorithm for the matroids in $M$.
Huynh, Tony, Nelson, Peter
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On Some Algorithmic and Structural Results on Flames
Journal of Graph Theory, Volume 110, Issue 4, Page 392-397, December 2025.ABSTRACT A directed graph F with a root node r is called a flame if for every vertex v other than r the local edge‐connectivity value λ F ( r , v ) from r to v is equal to ϱ F ( v ), the in‐degree of v. It is a classic, simple and beautiful result of Lovász [4] that every digraph D with a root node r has a spanning subgraph F that is a flame and the λ (
Dávid Szeszlér
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Rigidity through a Projective Lens
Applied Sciences, 2021 In this paper, we offer an overview of a number of results on the static rigidity and infinitesimal rigidity of discrete structures which are embedded in projective geometric reasoning, representations, and transformations.
Anthony Nixon +2 more
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Maximum size binary matroids with no AG(3,2)-minor are graphic [PDF]
, 2013 We prove that the maximum size of a simple binary matroid of rank $r \geq 5$ with no AG(3,2)-minor is $\binom{r+1}{2}$ and characterise those matroids achieving this bound.
Kung, Joseph P. S. +3 more
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An introduction to coding sequences of graphs
, 2016 In his pioneering paper on matroids in 1935, Whitney obtained a characterization for binary matroids and left a comment at end of the paper that the problem of characterizing graphic matroids is the same as that of characterizing matroids which ...
Ghosh, Shamik +2 more
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Girth in GF(q)$\textsf {GF}(q)$‐representable matroids
Bulletin of the London Mathematical Society, Volume 57, Issue 11, Page 3401-3407, November 2025.Abstract We prove a conjecture of Geelen, Gerards, and Whittle that for any finite field GF(q)$\textsf {GF}(q)$ and any integer t$t$, every cosimple GF(q)$\textsf {GF}(q)$‐representable matroid with sufficiently large girth contains either M(Kt)$M(K_t)$ or M(Kt)∗$M(K_t)^*$ as a minor.
James Davies +4 more
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