Results 81 to 90 of about 14,016 (208)
Generic root counts and flatness in tropical geometry
Journal of the London Mathematical Society, Volume 111, Issue 5, May 2025.Abstract We use tropical and nonarchimedean geometry to study the generic number of solutions of families of polynomial equations over a parameter space Y$Y$. In particular, we are interested in the choices of parameters for which the generic root count is attained.
Paul Alexander Helminck, Yue Ren
wiley +1 more source
Projective geometries in exponentially dense matroids. II [PDF]
, 2013 We show for each positive integer $a$ that, if $\mathcal{M}$ is a minor-closed class of matroids not containing all rank-$(a+1)$ uniform matroids, then there exists an integer $c$ such that either every rank-$r$ matroid in $\mathcal{M}$ can be covered by
Nelson, Peter
core
Efficient and strategy‐proof mechanism under general constraints
Theoretical Economics, Volume 20, Issue 2, Page 481-509, May 2025.This study investigates efficient and strategy‐proof mechanisms for allocating indivisible goods under constraints. First, we examine a setting without endowments. In this setting, we introduce a class of constraints—ordered accessibility—for which the serial dictatorship (SD) mechanism is Pareto‐efficient (PE), individually rational (IR), and group ...
Kenzo Imamura, Yasushi Kawase
wiley +1 more source
Rough matroids based on coverings [PDF]
, 2013 The introduction of covering-based rough sets has made a substantial contribution to the classical rough sets. However, many vital problems in rough sets, including attribution reduction, are NP-hard and therefore the algorithms for solving them are ...
Yang, Bin, Zhao, Hong, Zhu, William
core
The Projectivization Matroid of a $q$-Matroid
, 2022 In this paper, we investigate the relation between a $q$-matroid and its associated matroid called the projectivization matroid. The latter arises by projectivizing the groundspace of the $q$-matroid and considering the projective space as the groundset of the associated matroid on which is defined a rank function compatible with that of the $q ...
openaire +3 more sources
New building blocks for F1${\mathbb {F}}_1$‐geometry: Bands and band schemes
Journal of the London Mathematical Society, Volume 111, Issue 4, April 2025.Abstract We develop and study a generalization of commutative rings called bands, along with the corresponding geometric theory of band schemes. Bands generalize both hyperrings, in the sense of Krasner, and partial fields in the sense of Semple and Whittle.
Matthew Baker +2 more
wiley +1 more source
Broken Circuits in Matroids—Dohmen’s Inductive Proof
Discussiones Mathematicae Graph Theory, 2013 Dohmen [4] gives a simple inductive proof of Whitney’s famous broken circuits theorem.
Kordecki Wojciech +1 more
doaj +1 more source
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
European Journal of Combinatorics, 2001 20 pages.
Department of Mathematics, UMIST, PO Box 88, Manchester M60 1QD, U.K. f1 richard.booth@umist.ac.uk f1 f2 alexandre.borovik@umist.ac.uk f2 ( host institution ) +4 more
openaire +3 more sources
Basilica: New canonical decomposition in matching theory
Journal of Graph Theory, Volume 108, Issue 3, Page 508-542, March 2025.Abstract In matching theory, one of the most fundamental and classical branches of combinatorics, canonical decompositions of graphs are powerful and versatile tools that form the basis of this theory. However, the abilities of the known canonical decompositions, that is, the Dulmage–Mendelsohn, Kotzig–Lovász, and Gallai–Edmonds decompositions, are ...
Nanao Kita
wiley +1 more source