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

##
###
Colorful partitions of cardinal numbers

1979
*
Canadian Journal of Mathematics - Journal Canadien de Mathematiques
*

The letters K, X, p, Y, k, n, are reserved for

doi:10.4153/cjm-1979-056-4
fatcat:p352iwuh6rbepinintqvqav7te
*cardinal**numbers*, while 01, 0, y, 6, n, b are used for ordinals. Each ordinal*number*is identified with the set*of*its predecessors. ... N ow S induces a*partition**of*X = U(B,:a <cfp},whereB, = (y:S(y) =ai.Foreachcr<cfp,Rrestrictedto X X & maps into A,. ...##
###
Cardinal numbers with partition properties

1970
*
Bulletin of the Australian Mathematical Society
*

A

doi:10.1017/s0004972700045779
fatcat:atvz2hzc4baaxgt2d5mwwh74eq
*number**of*important open questions remain, however. The final chapter, Chapter V, is unrelated to the earlier ones. This is concerned with a development*of*the forcing method*of*P.J. ... Chapters II and IV are concerned with the generalization*of*the relation (l), a generalization obtained by considering not*partitions**of*the n-element subsets*of*K , but rather*partitions**of*certain finite ...*Cardinal**numbers*with*partition*properties Neil H. ...##
###
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. ... We introduce the b-domatic*number*bd(G) as the counterpart*of*the b-chromatic*number*by giving an alternative definition*of*the maximality*of*a*partition*into dominating sets. ... 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 ...##
###
An order property of partition cardinals

1970
*
Bulletin of the Australian Mathematical Society
*

This note studies

doi:10.1017/s0004972700045834
fatcat:fyijunszyzcdtgcd5zmhjgfbbe
*cardinal**numbers*K which have a*partition*property which amounts to the following. Let V be a*cardinal*, H an ordinal limit*number*and m a positive integer. ... The set*of*all finite subsets*of*S is denoted [ S ] < u .*Cardinal**numbers*are identified with the initial ordinals. ... Let K and v be*cardinals*, let n be an ordinal limit*number*and let m be a positive integer. Suppose that for any*partition*A = {A, ; I < v}*of*K into v parts the following situation prevails. ...##
###
Dualization of the van Douwen diagram

2000
*
Journal of Symbolic Logic (JSL)
*

AbstractWe make a more systematic study

doi:10.2307/2586580
fatcat:5g7r2ioxkbgjlp3zemne6gsxlu
*of*the van Douwen diagram for*cardinal*coefficients related to combinatorial properties*of**partitions**of*natural*numbers*. ... With any*partition*X e (co) we can consider some finite modification*of*X, denoted by X* 9 which is a*partition*obtained from X by gluing together a finite*number**of*pieces*of*X. ... coefficient t, i.e. the minimal*cardinal**number*being the*cardinality**of*a family well-ordered by the inverse almost containedness without lower bounds. ...##
###
Crossings and nestings in set partitions of classical types

2010
*
Discrete Mathematics & Theoretical Computer Science
*

On the other hand we generalize a bijection to type $B$ and $C$ that interchanges the

doi:10.46298/dmtcs.2826
fatcat:3dfg4xzokffetgxaixgf5nuhou
*cardinality**of*a maximal crossing with the*cardinality**of*a maximal nesting, as given by Chen, Deng, Du, Stanley and ... International audience In this extended abstract, we investigate bijections on various classes*of*set*partitions**of*classical types that preserve openers and closers. ... Stanley [4] have shown that the*number**of*set*partitions*where a maximal crossing has*cardinality*k and a maximal nesting has*cardinality*is the same as the*number**of*set*partitions*where a maximal crossing ...##
###
On shattering, splitting and reaping partitions
[article]

2001
*
arXiv
*
pre-print

Using some properties

arXiv:math/0109099v1
fatcat:ekkttasrujcjhe4a5pnogybhay
*of*the ideal J*of*nowhere dual-Ramsey sets, which is an ideal over the set*of**partitions**of*omega, we show that add(J)=cov(J)=H. ... In this article we investigate the dual-shattering*cardinal*H, the dual-splitting*cardinal*S and the dual-reaping*cardinal*R, which are dualizations*of*the well-known*cardinals*h (the shattering*cardinal*... The*cardinal**number*wS is the least*cardinal**number*κ, for which there exists a weak splitting family*of**cardinality*κ. (It is obvious that wS ≤ S ′ .) ...##
###
Chains, Antichains, and Complements in Infinite Partition Lattices
[article]

2017
*
arXiv
*
pre-print

Moreover, we give a direct formula for the

arXiv:1501.05284v4
fatcat:rqkjpehqxra63efgpujgsre57i
*number**of*complements to a given*partition*; (VI) Under the Generalized Continuum Hypothesis, the*cardinalities**of*maximal chains, maximal antichains, and*numbers*... Moreover we can construct maximal antichains*of**cardinality*(κ, 2^λ) for any λ<κ; (V) all*cardinals**of*the form κ^λ with 0 <λ<κ occur as the*number**of*complements to some*partition*P∈Π_κ, and only these ... James Avery was supported by VILLUM FONDEN through the network for Experimental Mathematics in*Number*Theory, Operator Algebras, and Topology. ...##
###
Page 2276 of Mathematical Reviews Vol. , Issue 83f
[page]

1983
*
Mathematical Reviews
*

*of*

*cardinality*« such that all the increasing sequences

*of*elements

*of*C lie in the same part

*of*the

*partition*. ... power set

*of*every ordinal exists, and there are arbitrarily large

*cardinals*with the strong

*partition*property. ...

##
###
Using partitions to characterize the minimum cardinality of an unbounded family in ωω

1990
*
Journal of combinatorial theory. Series A
*

Suppose v is an infinite

doi:10.1016/0097-3165(90)90027-t
fatcat:lnkbb3d7rbb5new4pkder2lizi
*cardinal*. We use the term "*partition*" to refer to a*partition**of*v with a countably intinite*number**of*cells. ...*Cardinal**numbers*. With respect to "CO partially ordered by < *, let b be the minimum*cardinality**of*an unbounded family, and let a' be the minimum*cardinality**of*a dominant (colinal) family. ...##
###
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*. ...

##
###
On partitions of discrete boxes

2002
*
Discrete Mathematics
*

We prove that any

doi:10.1016/s0012-365x(02)00428-4
fatcat:gsi3xpnyhnfthcf5lqhqcn5spq
*partition**of*an n-dimensional discrete box into nontrivial sub-boxes must consist*of*at least 2 n sub-boxes, and consider some extensions*of*this theorem. ... We are also grateful to Jeff Kahn for suggesting the point*of*view taken in subsection 2.4. ... A sub-box is odd if and only if each*of*its n factors has odd*cardinality*, and the nontriviality*of*the B j implies that half*of*the odd*cardinality*subsets*of*A i intersect B j i in an odd*number**of*elements ...##
###
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*. ...

##
###
A complete anytime algorithm for balanced number partitioning
[article]

1999
*
arXiv
*
pre-print

the

arXiv:cs/9903011v1
fatcat:iuuajo6yfrhuzfjhwul4xxpwnq
*cardinalities**of*the subsets be within one*of*each other. ... Given a set*of**numbers*, the balanced partioning problem is to divide them into two subsets, so that the sum*of*the*numbers*in each subset are as nearly equal as possible, subject to the constraint that ... The*numbers*in small font are the effective*cardinalities*needed to keep track*of*the*cardinality*difference*of*the final*partition*. The dashed parts*of*the tree are pruned by the algorithm. ...##
###
Cached Iterative Weakening for Optimal Multi-Way Number Partitioning

2014
*
PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE
*

The NP-hard

doi:10.1609/aaai.v28i1.9122
fatcat:34qwpmrskbenrjzijzuxn2d52m
*number*-*partitioning*problem is to separate a multiset S*of*n positive integers into k subsets, such that the largest sum*of*the integers assigned to any subset is minimized. ... instead*of*at each node*of*the search tree; and explores subsets in*cardinality*order instead*of*an arbitrary order. ... While*number**partitioning*fixes the*number**of*subsets k and minimizes the sum*of*the largest subset, bin packing fixes the maximum sum*of*the subsets (bins) and minimizes the*number**of*subsets needed. ...
« Previous

*Showing results 1 — 15 out of 139,065 results*