A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Partitioning into Sets of Bounded Cardinality
[chapter]

2009
*
Lecture Notes in Computer Science
*

We show that the

doi:10.1007/978-3-642-11269-0_21
fatcat:abr6k7xxsncepfcdtnl4bplkau
*partitions**of*an n-element*set*into k members*of*a given*set*family can be counted in time O((2− ) n ), where > 0 depends only on the maximum size among the members*of*the family. ... Lemma 1 . 1 The number*of**partitions**of*N into k members*of*F equals the*cardinality**of*L k . Lemma 3 . 3 Let n and r be natural numbers. ... In this paper, we answer the question affirmatively in the special case where the given*set*family consists*of**sets*whose*cardinality*is bounded by a constant. ...##
###
A parallel algorithm for iterating partitions of a finite set into subsets of a given cardinality

2020
*
Vestnik of Saint Petersburg University Applied Mathematics Computer Science Control Processes
*

The first algorithm for each element

doi:10.21638/11702/spbu10.2020.105
fatcat:bshbnsfzb5cfbi2upjbrofqt6m
*of*the original*set*determines the*cardinality**of*the subset that it will fall into when*partitioning*. ... -мат. наук, доц.; a.kovshov@spbu.ru A parallel algorithm for iterating*partitions**of*a finite*set*into subsets*of*a given*cardinality*A. M. Kovshov St. ...##
###
Page 3434 of Mathematical Reviews Vol. , Issue 87g
[page]

1987
*
Mathematical Reviews
*

The expression a — (3); means that for every

*partition**of*the*set*[A]”*of*r-element subsets*of*a*set*A*of**cardinality*a into 6 pieces, there is a*set*B*of**cardinality*6 with all its r-element subsets in ... For example, if A is an uncountable*cardinal*, can we guarantee the existence*of*a homogeneous*set**of*the same*cardinality*as A for every*partition**of*the n-element subsets*of*A? ...##
###
Some remarks on Kuratowski partitions
[article]

2017
*
arXiv
*
pre-print

We introduce the notion

arXiv:1706.08828v1
fatcat:36ks7yarufacxgt2swb6vg42ee
*of*K-ideals associated with Kuratowski*partitions*and we prove that each κ-complete ideal on a measurable*cardinal*κ can be represented as a K-ideal. ... We are very grateful for Reviewers and Editors who had the big influence*of*the final version*of*this paper. Some remarks on Kuratowski*partitions*... Definitions and basic facts Let X be a topological space and let κ be a regular*cardinal*. Let F be a*partition**of*X into meager*sets*. ...##
###
On special partitions of metric spaces
[article]

2020
*
arXiv
*
pre-print

The main result

arXiv:2003.11017v4
fatcat:vkcnnhdkpbdp3aicvukhptzpdu
*of*this paper is to show that, if κ is the smallest real-valued measurable*cardinal*not greater than 2^ℵ_0, then there exists a complete metric space*of**cardinality*not greater than 2^κ ... admitting a Kuratowski*partition*. ... Let F be a K-*partition**of*X*of**cardinality*κ. Let I F be a K-ideal associated with F . By Fact 1, there exists a non-empty open*set*U ⊆ X such that I F ∩U is a precipitous ideal. ...##
###
The b-domatic number of a graph

2013
*
Discussiones Mathematicae Graph Theory
*

A

doi:10.7151/dmgt.1709
fatcat:tb3cgqvvo5fjho46zponoq65da
*partition*P*of*G is a*partition**of*its vertex*set*V . Its*cardinality*|P| is the number*of*classes*of*P. ... A dominating*set*is divisible if it contains two disjoint dominating*sets**of*G, indivisible otherwise. We denote by ω(G) the maximum*cardinality**of*a clique*of*G. ... The authors*of*[10] solved the interpolation problem for the a-chromatic number by proving that every graph G admits a-minimal chromatic*partitions**of*any ...##
###
The new operations on complete ideals

2019
*
Open Mathematics
*

We introduce the notion

doi:10.1515/math-2019-0032
fatcat:gzwuurmkq5e47cmfjdhlkydvgq
*of*K-ideals associated with Kuratowski*partitions*. ... Acknowledgement: The author is very grateful to the Reviewers for their comments which have raised the quality*of*this text and allowed to avoid many errors and inaccuracies. ... The concept*of*Kuratowski*partitions*emerged when attempting to solve the problem*set*by K. ...##
###
Weak partition properties for infinite cardinals. I

1971
*
Proceedings of the American Mathematical Society
*

*Partition*properties are perhaps the most fruitful

*of*the various methods for defining and discussing large

*cardinals*in

*set*theory. ... In this paper we weaken in a natural way the most well known

*of*these

*partition*properties and examine the extent to which the

*cardinals*defined remain "large." ... An area

*of*

*set*theory which has come under a great deal

*of*study recently is that concerned with

*partition*properties for

*cardinal*numbers. ...

##
###
Weak Partition Properties for Infinite Cardinals. I

1971
*
Proceedings of the American Mathematical Society
*

*Partition*properties are perhaps the most fruitful

*of*the various methods for defining and discussing large

*cardinals*in

*set*theory. ... In this paper we weaken in a natural way the most well known

*of*these

*partition*properties and examine the extent to which the

*cardinals*defined remain "large." ... An area

*of*

*set*theory which has come under a great deal

*of*study recently is that concerned with

*partition*properties for

*cardinal*numbers. ...

##
###
Page 1527 of Mathematical Reviews Vol. 46, Issue 6
[page]

1973
*
Mathematical Reviews
*

Say that a

*set*is hereditarily*of**cardinality*<y if (Vy eZ) (card(y) <y). Denote by V, the class*of*all*sets*hereditarily*of**cardinality*<y. ... Symbolic Logic 35 (1970), 410-428. 8839 The notation «—>(«)*, where « is a*cardinal*and « is an ordinal <x, means that whenever the*set**of*increasing a-sequences*of*elements*of*« is*partitioned*into two ...##
###
Connections between Kuratowski partitions of Baire spaces, measurable cardinals and precipitous ideals
[article]

2022
*
arXiv
*
pre-print

In this paper we present a few properties

arXiv:2205.12653v1
fatcat:s7bqa7wkmfh3ng5zasb34fzv24
*of*K-*partitions*, which are*partitions**of*Baire spaces such that all subfamilies*of*such a*partition*sum to a*set*with the Baire property. ... We also prove some connections between existence*of*K-*partitions*and existence*of*precipitous ideals as well as measurable*cardinals*. ... The saturation*of*I -denoted by sat(I) -is the smallest*cardinal*such that all antichains in Y /I are*of**cardinality*less than sat(I). Definition 4. Let I be an ideal on a*set*Y . ...##
###
Bounds on the cardinality of partition
[article]

2018
*
arXiv
*
pre-print

Let
Part A be the collection

arXiv:0711.2241v9
fatcat:lfngxxtl55cwdh5x4zblvj3rsi
*of**partitions**of*a*set*A . ... INTRODUCTION A*partition**of*a*set*A is a collection*of*nonempty disjoint subsets*of*A whose union is Since this*partition*is unique, g is an injection. A . ...##
###
Book Review: Combinatorial set theory

1979
*
Bulletin of the American Mathematical Society
*

Globally, I very much like the spirit and the scope

doi:10.1090/s0273-0979-1979-14558-0
fatcat:5ram2bxhznenvbhcp7rniznjcm
*of*the book. ... Locally, more attention could have been paid to detail; there are many misprints, some mistatements*of*results, and some proofs need tightening. ... Given*cardinals*K, À, and /x, and a positive integer «, the*partition*relation means that if A is a*set**of**cardinality*K and the*set*[A] n*of*(unordered) «-element subsets*of*A is*partitioned*into p pieces ...##
###
Page 1274 of Mathematical Reviews Vol. , Issue 95c
[page]

1995
*
Mathematical Reviews
*

In Section 2 they extend this relation to

*partitions**of*the*set**of*all finite sequences in L,,.,,(A1 x --- x An), for an infinite sequence*of**cardinals*/;, A2,---. ... The polarized*partition*relation with these*cardinals*as parameters holds provided that for every*partition**of*the Cartesian product A; x --- x A, into d parts, there is a sequence*of**sets*H; € [A;]*', ...##
###
A Comparison of Pair and Triple Partition Relations
[article]

2019
*
arXiv
*
pre-print

This paper considers three different

arXiv:1904.07790v1
fatcat:d2z5xcrc5nfxrf7a2mkgtbi6om
*partition*relations from*partition*calculus, two*of*which are pair relations and one*of*which is a triple relation. ... An examination*of*the first*partition*relation and the ramification argument used to prove it will motivate questions regarding how to strengthen it. ... Definition 8 (*Partitions*). For X a*set*and I an indexing*set*, a*partition**of*X in I colors is a function χ : X → I. An r-*partition**of*X in I colors is a*partition**of*[X] r in I colors. ...
« Previous

*Showing results 1 — 15 out of 142,575 results*