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

##
###
The covering lemma for K

1982
*
Annals of Mathematical Logic
*

t(~

doi:10.1016/0003-4843(82)90013-4
fatcat:cwvriq3u6vcdbj7boujaqezb3m
*the**covering**lemma**for*L. ... to pre,~ent these last two results in a .3eparate paper "*The**covering**lemma**for*L[U]". ...*The*result is true even without (b) but ~he proof is more involved, and*the*stated result suffices*for**the**covering**lemma*. Section 3 contains some messy technicalities about well foundedness. ...##
###
Periodic orbits of continuous mappings of the circle

1980
*
Transactions of the American Mathematical Society
*

It is shown that if 1 G P(f) and n G P(f)

doi:10.1090/s0002-9947-1980-0574798-8
fatcat:vocdgthdmvde3kcgt3uwng7zle
*for*some odd positive integer n then*for*every integer m > n, m G P(f). ... Let / be a continuous map of*the*circle into itself and let P(f) denote*the*set of positive integers n such that/has a periodic point of period n. ... Suppose that*for*some positive integery with s < / < ^ -1, L /-*covers*T". Then*the*conclusion of*the*theorem holds by*Lemma*7 (with*k*= 3, Mx = [e,px], M2 = Tr_, and M3 = IJ). ...##
###
Periodic Orbits of Continuous Mappings of the Circle

1980
*
Transactions of the American Mathematical Society
*

It is shown that if 1 G P(f) and n G P(f)

doi:10.2307/1998021
fatcat:rewhnghnkjcxbgfhaoxccprqci
*for*some odd positive integer n then*for*every integer m > n, m G P(f). ... Let / be a continuous map of*the*circle into itself and let P(f) denote*the*set of positive integers n such that/has a periodic point of period n. ... Suppose that*for*some positive integery with s < / < ^ -1, L /-*covers*T". Then*the*conclusion of*the*theorem holds by*Lemma*7 (with*k*= 3, Mx = [e,px], M2 = Tr_, and M3 = IJ). ...##
###
Upper bounds on the sizes of variable strength covering arrays using the Lovász local lemma
[article]

2019
*
arXiv
*
pre-print

is

arXiv:1901.05386v2
fatcat:bfikset3h5hftg5q22szxv276i
*the*special case where coverage is required*for*all sets of columns of a fixed size t, its strength. ...*The*conclusions are dependent on*the*class of hypergraph, and we discuss specific characteristics of*the*hypergraphs which are more amenable to using different versions of*the*Lovász local*lemma*. ...*The*authors would like to thank an anonymous reviewer*for*various suggestions that improved*the*presentation of this paper. ...##
###
On coverings

1964
*
Pacific Journal of Mathematics
*

*The*existence of an admissible

*covering*M(

*k*-1, 1,1, n) is obvious. Suppose now that

*the*

*lemma*is proved

*for*I -l 0 and let I -l 0 + 1. ...

*coverings*which are not tactical configurations*

*The*fact that there exist admissible

*coverings*which are not tactical configurations will be shown in Corollaries 1, 2 and 3 to

*Lemma*3, but

*for*

*the*purpose ...

##
###
Quasi-Differential Posets and Cover Functions of Distributive Lattices

2000
*
Journal of combinatorial theory. Series A
*

A function f : N 0 Ä N 0 is a

doi:10.1006/jcta.1999.3021
fatcat:43vdd3wunbdnhkzd5wmpwto7ru
*cover*function*for*L if every element with n lower*covers*has f (n) upper*covers*. ... In this paper, all finitary distributive lattices with non-decreasing*cover*functions are characterized. A 1975 conjecture of Richard P. Stanley is thereby settled. Academic Press ... Example 3 . 2 . 32*For**k*# N,*the*function f (n)=*k*+n (n # N 0 ) is a*cover*function*for*Y*k*. (See*Lemma*4.8.) Example 3.3. ...##
###
On Ryser's conjecture

2012
*
Electronic Journal of Combinatorics
*

Motivated by an old problem known as Ryser's Conjecture, we prove that

doi:10.37236/1175
fatcat:ohwf5udiknhczmrs5y5lk26io4
*for*$r=4$ and $r=5$, there exists $\epsilon>0$ such that every $r$-partite $r$-uniform hypergraph $\cal H$ has a*cover*of size at ... most $(r-\epsilon)\nu(\cal H)$, where $\nu(\cal H)$ denotes*the*size of a largest matching in $\cal H$. ...*For*each x*k*that exists and lies in a*cover*of size two of*the*C l it is in, set z*k*to be*the*other vertex of*the**cover*. Note that z*k*is unique by*Lemma*2.3. Define z*k*similarly*for*each x*k*. ...##
###
Covering Numbers in Linear Algebra
[article]

2012
*
arXiv
*
pre-print

We compute

arXiv:1208.0975v1
fatcat:zpmmi5bz65bxfkylxew3zcybqq
*the*minimal cardinality of a*covering*(resp. an irredundant*covering*) of a vector space over an arbitrary field by proper linear subspaces. ... Analogues*for*affine linear subspaces are also given. ...*Lemma*2.*For*any field*K*,*the*unique linear*covering*of*K*2 is*the*set of all lines through*the*origin, of cardinality #*K*+ 1. It is an irredundant*covering*. Proof. ...##
###
Combinatorial Theorems on the Simplotope that Generalize Results on the Simplex and Cube

1986
*
Mathematics of Operations Research
*

Each combinatorial theorem also implies set

doi:10.1287/moor.11.1.169
fatcat:hw5khefj7vf6diqijznausqpdm
*covering**lemmas*on*the*simplotope,*the*simplex, and*the*cube, including*the*Generalized*Covering**lemma*,*the*Knaster-Kuratowski-Mazurkiewicz*lemma*, and a*lemma*... This paper presents three combinatorial theorems on*the*simplotope, and shows how each translates into some known and new results on*the*simplex and cube, including various forms of Sperner's*lemma*. ...*For**the*details of*the*proof, Cn I vk = 1,*k*= 1,..., n. Then there exists j e {1,..., nI such that Di n D j # I.*Covering**lemma*3 on*the*Cube: Let D ,...,*Covering**lemma*2 on*the*Cube, n = 2. ...##
###
Small cycle covers of 3-connected cubic graphs

2011
*
Discrete Mathematics
*

It is proved in this paper that G admits a cycle

doi:10.1016/j.disc.2010.10.013
fatcat:umi3qzbhe5gipc3bmfpztikltm
*cover*of size at most ⌈n/6⌉ if and only if G is not one of*the*five specified graphs. ... Acknowledgements*The*authors would like to thank*the*referees*for**the*valuable comments and suggestions which improved*the*representation. ...*The*second author is partially supported by*the*Natural Science Foundation of China (10571071),*the*Research Funds of CCNU09Y01018, and Hubei Key Laboratory of Mathematical Sciences of China. ...##
###
Covering Numbers in Linear Algebra

2012
*
The American mathematical monthly
*

We compute

doi:10.4169/amer.math.monthly.119.01.065
fatcat:dmjdl4qk3rbc5ebswkvrbykq3m
*the*minimal cardinality of a*covering*(resp. an irredundant*covering*) of a vector space over an arbitrary field by proper linear subspaces. ... Analogues*for*affine linear subspaces are also given. ...*Lemma*2 . 2*For*any field*K*,*the*unique linear*covering*of*K*2 is*the*set of all lines through*the*origin, of cardinality #*K*+ 1. It is an irredundant covering.Proof. ...##
###
Subdirect products and covering groups by subgroups

2013
*
International Journal of Algebra
*

A

doi:10.12988/ija.2013.3434
fatcat:tr6tloy5ovgyjay36xhsr3dwcq
*cover**for*a group is a collection of proper subgroups whose union is*the*whole group. ... A*cover*C*for*a group G is called a C n -*cover*whenever C is an irredundant maximal core-free n-*cover**for*G and in this case we say that G is a C n -group. ... A set C of proper subgroups of G is called a*cover**for*G if its set-theoretic union is equal to G. If*the*size of C is n, we call C an n-*cover**for**the*group G. ...##
###
On uniform approximation of harmonic functions

2012
*
St. Petersburg Mathematical Journal
*

*The*result is an approximation theorem

*for*an individual function under

*the*condition that, on

*the*complement to

*the*compact set,

*the*harmonic capacity is "homogeneous" in a sense. ...

*The*proof involves a refinement of Vitushkin's localization method. §0. Introduction Let X ⊂ R 3 be a compact set, X •

*the*interior of X, Δ

*the*Laplace operator in R 3 . ... )) (see

*Lemma*1.5) that corresponds to

*the*new

*Cover*(ν); furthermore,

*k*7 depends only on

*k*0 in (0.2) and on

*k*2 in

*Lemma*1.5. ...

##
###
Volumes of balls in Riemannian manifolds and Uryson width
[article]

2015
*
arXiv
*
pre-print

If (M^n, g) is a closed Riemannian manifold where every unit ball has volume at most ϵ_n (a sufficiently small constant), then

arXiv:1504.07886v1
fatcat:afgw5ngosbddlh4cyeqo5tubza
*the*(n-1)-dimensional Uryson width of (M^n, g) is at most 1. ... Our map φ (*k*−1) will be R δ(*k*) •φ (*k*)*for*a well-chosen δ(*k*). Notice that*for*any δ,*the*map R δ sends each open face F intoF . By*Lemma*1.1, R δ •φ (*k*) is subordinate to*the**cover*. ... In particular, we get*the*following*lemma*.*Lemma*1.2. Suppose that φ (*k*) : X → N (*k*) is a map from X to*the**k*-skeleton of N subordinate to*the**cover*. ...##
###
Local colourings and monochromatic partitions in complete bipartite graphs

2017
*
European journal of combinatorics (Print)
*

We show that

doi:10.1016/j.ejc.2016.09.003
fatcat:idxj4cq3anatlgzjfblbl4vshi
*for*any 2-local colouring of*the*edges of a complete bipartite graph, its vertices can be*covered*with at most 3 disjoint monochromatic paths. ... And, we can*cover*almost all vertices of any complete or complete bipartite r-locally coloured graph with O(r 2 ) disjoint monochromatic cycles. ... In total, we used r(r + 1)/2 + r 2 + 1 ≤ 2r 2 disjoint monochromatic cycles to*cover*all of*K*n . This proves Theorem 1.1(a). ...
« Previous

*Showing results 1 — 15 out of 368,420 results*