Result: Maximal Sidon sets and matroids
Title:
Maximal Sidon sets and matroids
Authors:
Source:
Discrete mathematics. 309(13):4489-4494
Publisher Information:
Kidlington: Elsevier, 2009.
Publication Year:
2009
Physical Description:
print, 7 ref
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Combinatoire. Structures ordonnées, Combinatorics. Ordered structures, Ordre, treillis, structures algébriques ordonnées, Order, lattices, ordered algebraic structures, Algèbre, Algebra, Théorie des nombres, Number theory, Théorie des groupes, Group theory, Théorie des groupes et généralisations, Group theory and generalizations, Géométrie, Geometry, Géométrie convexe et discrète, Convex and discrete geometry, Ensemble ordonné, Ordered set, Conjunto ordenado, Groupe abélien, Abelian group, Grupo abeliano, Intersection, Intersección, Matroïde, Matroid, Matroide, Théorie nombre, Number theory, Teoría números, 06Axx, 11Pxx, 11xx, 20Kxx, 52B40, Cardinalité, Multiensemble, Additive number theory, Bh-sets, Combinatorial number theory, Sidon sets
Document Type:
Academic journal
Article
File Description:
text
Language:
English
Author Affiliations:
Departamento de Matemática, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Bloco C6, 1749-016 Lisboa, Portugal
Department of Mathematics, Lehman College (CUNY), Bronx, NY 10468, United States
Department of Mathematics, Lehman College (CUNY), Bronx, NY 10468, United States
ISSN:
0012-365X
Rights:
Copyright 2009 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.21543974
Database:
PASCAL Archive
Further Information
A subset X of an abelian group Γ, written additively, is a Sidon set of order h if whenever {(ai, mi): i ∈ I} and ((bj, nj): j ∈ J} are multisets of size h with elements in X and Σi∈I m¡a¡ = Σj∈J njbj, then {(ai, mi): i ∈ I} = {(bj, nj): j ∈ J}. The set X is ageneralized Sidon set of order (h, k) if whenever two such multisets have the same sum, then their multiset intersection has size at least k. It is proved that if X is a generalized Sidon set of order (2h ― 1, h ― 1), then the maximal Sidon sets of order h contained in X have the same cardinality. Moreover, X is a matroid where the independent subsets of X are the Sidon sets of order h.