scholarly journals Combinatorial property of all positive measures in dimensions $2$ and $3$

2020 ◽  
Vol 358 (6) ◽  
pp. 721-725
Author(s):  
Pavel Mozolyako ◽  
Georgios Psaromiligkos ◽  
Alexander Volberg ◽  
Pavel Zorin Kranich
Keyword(s):  
Combinatorial Property

A Combinatorial Property of Measurable Cardinals

1974 ◽  
Vol 20 (7) ◽  
pp. 109-111 ◽  
Author(s):  
E. M. Kleinberg
Keyword(s):  
Combinatorial Property ◽  
Measurable Cardinals

A combinatorial property and growth for semigroups of matrices

1998 ◽  
Vol 26 (9) ◽  
pp. 2789-2805 ◽  
Author(s):  
A.V. Kelarev ◽  
J. Okniński
Keyword(s):  
Combinatorial Property

Combinatorial Property of a Special Polynomial Sequence

1977 ◽  
Vol 20 (2) ◽  
pp. 183-188 ◽  
Author(s):  
L. Carlitz
Keyword(s):  
Combinatorial Property ◽  
Polynomial Sequence ◽  
Special Polynomial ◽  
Image Position

Leeming [4] has defined a sequence of polynomials {Q4n(x)} and a sequence of integers {Q4n} by means of1and2Thus3Leeming showed that the Q4n are all odd and that4It is proved in [3] that5

A combinatorial property of pκλ

1976 ◽  
Vol 41 (1) ◽  
pp. 225-234
Author(s):  
Telis K. Menas
Keyword(s):  
Large Cardinals ◽  
Combinatorial Property ◽  
Combinatorial Properties ◽  
Partition Property ◽  
Homogeneous Set ◽  
Unbounded Subset

In a paper on combinatorial properties and large cardinals [2], Jech extended several combinatorial properties of a cardinal κ to analogous properties of the set of all subsets of λ of cardinality less than κ, denoted by “pκλ”, where λ is any cardinal ≤κ. We shall consider in this paper one of these properties which is historically rooted in a theorem of Ramsey [10] and in work of Rowbottom [12].As in [2], define [pκλ]2 = {{x, y}: x, y ∈ pκλ and x ≠ y}. An unbounded subset A of pκλ is homogeneous for a function F: [pκλ]2 → 2 if there is a k < 2 so that for all x, y ∈ A with either x ⊊ y or y ⊊ x, F({x, y}) = k. A two-valued measure ü on pκλ is fine if it is κ-complete and if for all α < λ, ü({x ∈ pκλ: α ∈ x}) = 1, and ü is normal if, in addition, for every function f: pκλ → λsuch that ü({x ∈ pκλ: f(x) ∈ x}) = 1, there is an α < λ such that ü({x ∈ pκλ: f(x) = α}) = 1. Finally, a fine measure on pκλ has the partition property if every F: [pκλ]2 → 2 has a homogeneous set of measure one.

AVERAGE MEASURE, DESCRIPTIVE COMPLEXITY AND APPROXIMATION OF MAXIMIZATION PROBLEMS

1993 ◽  
Vol 04 (01) ◽  
pp. 15-30 ◽  
Author(s):  
PIERLUIGI CRESCENZI ◽  
RICCARDO SILVESTRI
Keyword(s):  
Optimization Problems ◽  
Combinatorial Property ◽  
Maximization Problem ◽  
Descriptive Complexity ◽  
Feasible Solutions ◽  
Average Measure

In this paper, we study a simple combinatorial property of maximization problems and we establish some interesting connections between such a property and the class [Formula: see text] defined by Papadimitriou and Yannakakis. In particular, we first prove that any maximization problem in [Formula: see text] has guaranteed average measure, that is, the average measure of the feasible solutions is no less than a constant fraction of the optimum measure (this intuitively justifies the fact that any problem in [Formula: see text] is approximable). Successively, we prove that there exist maximization problems that do not belong to [Formula: see text] but still have guaranteed average measure. Hence, such a property does not characterize the class [Formula: see text]. Finally, we show that there are several maximization problems which do not have guaranteed average measure and, hence, do not belong to [Formula: see text]. In this context, the notion of a problem with guaranteed average measure seems to be a powerful and very easy-to-use tool that allows us to prove that optimization problems are not in [Formula: see text].

scholarly journals On the partition property of measures onPℋλ

1982 ◽  
Vol 5 (4) ◽  
pp. 817-821
Author(s):  
Donald H. Pelletier
Keyword(s):  
Measurable Cardinal ◽  
Combinatorial Property ◽  
Partition Property ◽  
Normal Measure

The partition property for measures onPℋλwas formulated by analogy with a property which Rowbottom [1] proved was possessed by every normal measure on a measurable cardinal. This property has been studied in [2], [3], and [4]. This note summarizes [5] and [6], which contain results relating the partition property with the extendibility of the measure and with an auxiliary combinatorial property introduced by Menas in [4]. Detailed proofs will appear in [5] and [6].

scholarly journals On a combinatorial property of Fibonacci semigroup

1993 ◽  
Vol 122 (1-3) ◽  
pp. 263-267 ◽  
Author(s):  
Giuseppe Pirillo
Keyword(s):  
Combinatorial Property

Testing juntas [combinatorial property testing]

2003 ◽  
Author(s):  
E. Fischer ◽  
G. Kindler ◽  
D. Ron ◽  
S. Safra ◽  
A. Samorodnitsky
Keyword(s):  
Property Testing ◽  
Combinatorial Property
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