Results 51 to 60 of about 511 (171)
Valuations for Matroid Polytope Subdivisions
, 2010 We prove that the ranks of the subsets and the activities of the bases of a matroid define valuations for the subdivisions of a matroid polytope into smaller matroid polytopes.
Federico Ardila +2 more
core +1 more source
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
wiley +1 more source
Bases for permutation groups and matroids
European Journal of Combinatorics, 1995 If \(G\) is a permutation group acting on an \(n\)-set \(X\), then the bases of \(G\) are the sets of points of \(X\) that are (pointwise) fixed only by the identity of \(G\) (i.e., the sets with trivial stabilizer). An irredundant basis is an ordered basis such that no element is fixed by the joint stabilizer of the previous elements. It is shown that
Peter J. Cameron, Dmitry Fon-Der-Flaass
openaire +1 more source
Equivariant Hilbert and Ehrhart series under translative group actions
Journal of the London Mathematical Society, Volume 112, Issue 5, November 2025.Abstract We study representations of finite groups on Stanley–Reisner rings of simplicial complexes and on lattice points in lattice polytopes. The framework of translative group actions allows us to use the theory of proper colorings of simplicial complexes without requiring an explicit coloring to be given.
Alessio D'Alì, Emanuele Delucchi
wiley +1 more source
On Greedy Bases Packing in Matroids
European Journal of Combinatorics, 2002 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +1 more source
The natural matroid of an integer polymatroid
, 2022 The natural matroid of an integer polymatroid was introduced to show that a simple construction of integer polymatroids from matroids yields all integer polymatroids. As we illustrate, the natural matroid can shed much more light on integer polymatroids.
Chun, Carolyn +5 more
core +1 more source
Approximate‐Guided Representation Learning in Vision Transformer
CAAI Transactions on Intelligence Technology, Volume 10, Issue 5, Page 1459-1477, October 2025.ABSTRACT In recent years, the transformer model has demonstrated excellent performance in computer vision (CV) applications. The key lies in its guided representation attention mechanism, which uses dot‐product to depict complex feature relationships, and comprehensively understands the context semantics to obtain feature weights.
Kaili Wang +4 more
wiley +1 more source
On the Number of Bases of Almost All Matroids [PDF]
Combinatorica, 2018 18 pages, 2 ...
Pendavingh, Rudi, van der Pol, Jorn
openaire +4 more sources
A circle method approach to K‐multimagic squares
Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.Abstract In this paper, we investigate K$K$‐multimagic squares of order N$N$. These are N×N$N \times N$ magic squares that remain magic after raising each element to the k$k$th power for all 2⩽k⩽K$2 \leqslant k \leqslant K$. Given K⩾2$K \geqslant 2$, we consider the problem of establishing the smallest integer N2(K)$N_2(K)$ for which there exist ...
Daniel Flores
wiley +1 more source
On the number of circuit–cocircuit reversal classes of an oriented matroid [PDF]
, 2019 International audienceThe first author introduced the circuit–cocircuit reversal system of an oriented matroid, and showed that when the underlying matroid is regular, the cardinalities of such system and its variations are equal to special evaluations ...
Gioan, Emeric, Yuen, Chi Ho
core +1 more source