scholarly journals Combinatorial characterization of hexagonal systems

1988 ◽  
Vol 19 (1-3) ◽  
pp. 259-270 ◽  
Author(s):  
Antonije D. Javanovic
Keyword(s):  
Combinatorial Characterization ◽  
Hexagonal Systems

scholarly journals A Combinatorial Characterization of Jacobi Forms

2009 ◽  
Vol 39 (2) ◽  
pp. 455-462
Author(s):  
Youngju Choie ◽  
Olav K. Richter
Keyword(s):  
Jacobi Forms ◽  
Combinatorial Characterization

scholarly journals A combinatorial characterization of planar 2-complexes

1981 ◽  
Vol 44 (2) ◽  
pp. 241-247 ◽  
Author(s):  
Jonathan L. Gross ◽  
Ronald H. Rosen
Keyword(s):  
Combinatorial Characterization

A combinatorial characterization of treelike resolution space

2003 ◽  
Vol 87 (6) ◽  
pp. 295-300 ◽  
Author(s):  
Juan Luis Esteban ◽  
Jacobo Torán
Keyword(s):  
Combinatorial Characterization

Lebesque measure zero subsets of the real line and an infinite game

1996 ◽  
Vol 61 (1) ◽  
pp. 246-249 ◽  
Author(s):  
Marion Scheepers
Keyword(s):  
Lebesgue Measure ◽  
Real Line ◽  
Measure Zero ◽  
Cardinal Number ◽  
Minimal Cardinality ◽  
Combinatorial Characterization ◽  
The Real ◽  
Lebesque Measure ◽  
The Ideal

Let denote the ideal of Lebesgue measure zero subsets of the real line. Then add() denotes the minimal cardinality of a subset of whose union is not an element of . In [1] Bartoszynski gave an elegant combinatorial characterization of add(), namely: add() is the least cardinal number κ for which the following assertion fails:For every family of at mostκ functions from ω to ω there is a function F from ω to the finite subsets of ω such that:1. For each m, F(m) has at most m + 1 elements, and2. for each f inthere are only finitely many m such that f(m) is not an element of F(m).The symbol A(κ) will denote the assertion above about κ. In the course of his proof, Bartoszynski also shows that the cardinality restriction in 1 is not sharp. Indeed, let (Rm: m < ω) be any sequence of integers such that for each m Rm, ≤ Rm+1, and such that limm→∞Rm = ∞. Then the truth of the assertion A(κ) is preserved if in 1 we say instead that1′. For each m, F(m) has at most Rm elements.We shall use this observation later on. We now define three more statements, denoted B(κ), C(κ) and D(κ), about cardinal number κ.

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