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Independent finite sums in graphs defined on the natural numbers

1998
*
Discrete Mathematics
*

*In*particular, we prove that if k, f >~ 2 and a

*graph*G

*defined*

*on*

*the*

*natural*

*numbers*contains no copies of

*the*complete

*graph*

*on*k vertices, then there exists a subset A C ~ such that

*the*set FS~ no ... An infinite version of this problem was stated by Andr~ts Hajnal, who asked if, for a

*graph*G

*defined*

*on*

*the*set of

*natural*

*numbers*, there exists an infinite set A with

*the*above property. ...

*In*particular,

*the*set FS~<t(A) is

*independent*. ...

##
###
Independence densities of hypergraphs

2014
*
European journal of combinatorics (Print)
*

*In*

*the*case of

*finite*but unbounded hyperedges, we show that

*the*

*independence*density can be any real

*number*

*in*[0, 1]. ... We consider

*the*

*number*of

*independent*sets

*in*hypergraphs, which allows us to

*define*

*the*

*independence*density of countable hypergraphs. ...

*The*authors gratefully acknowledge support from NSERC, MPrime, and Ryerson University. ...

##
###
Independence densities of hypergraphs
[article]

2013
*
arXiv
*
pre-print

*In*

*the*case of

*finite*but unbounded hyperedges, we show that

*the*

*independence*density can be any real

*number*

*in*[0,1]. ... We consider

*the*

*number*of

*independent*sets

*in*hypergraphs, which allows us to

*define*

*the*

*independence*density of countable hypergraphs. ... We extend

*the*definition of

*independence*density of

*finite*hypergraphs

*in*

*the*

*natural*way to countable hypergraphs (which we

*define*to be

*on*a countable set of vertices but with edges of

*finite*cardinality ...

##
###
On Factor Graphs and the Fourier Transform

2005
*
IEEE Transactions on Information Theory
*

We use these function extensions to derive a

doi:10.1109/tit.2005.846404
fatcat:a3luxnr5frextpijbxullecqqm
*number*of duality relationships among*the*corresponding factor*graphs*, and use these relationships to obtain*the*duality properties of Forney*graphs*as a special ... Convolutional and multiplicative factor*graphs*arise as*natural*Fourier transform duals. ... These comments have resulted*in*a substantially improved paper. ...##
###
Page 5939 of Mathematical Reviews Vol. , Issue 89K
[page]

1989
*
Mathematical Reviews
*

*In*

*the*last section

*the*exponential growth

*number*of G is

*defined*

*in*

*the*case when G is infinite and locally

*finite*. ... It appears that this

*number*is related to

*the*essential isoperimetric

*number*of G,

*defined*by taking

*the*supremum of

*the*isoperimetric

*numbers*of

*graphs*ob- tained from G by adding or deleting

*finitely*...

##
###
The topology of graph products of groups

1994
*
Proceedings of the Edinburgh Mathematical Society
*

Given a

doi:10.1017/s001309150001899x
fatcat:dedq7im4n5eircdt5fapj7jkqe
*finite*(connected) simplicial*graph*with groups assigned to*the*vertices,*the**graph*product of*the*vertex groups is*the*free product modulo*the*relation that adjacent groups commute. ...*The**graph*product of*finitely*presented infinite groups is both semistable at infinity and quasi-simply filtrated. ... An isodiametric function for a presentation is a function I(n) from*the**natural**numbers*to*the**natural**numbers*, such that for*the*any set of words {co,} whose lengths*sum*to less than or equal to n, £i ...##
###
Nilpotent adjacency matrices, random graphs and quantum random variables

2008
*
Journal of Physics A: Mathematical and Theoretical
*

Each nilpotent adjacency matrix is a quantum random variable whose m th moment corresponds to

doi:10.1088/1751-8113/41/15/155205
fatcat:pbt56hdivfeavnz77fs6vhu5am
*the**number*of mcycles*in**the**graph*G. ... Using*the*generators of*the*subalgebra, an algebraic probability space of "nilpotent adjacency matrices" associated with*finite**graphs*is*defined*. ... A*graph*is*finite*if V and E are*finite*sets, that is, if |V | and |E| are*finite**numbers*. A loop*in*a*graph*is an edge of*the*form (v, v). ...##
###
Page 3591 of Mathematical Reviews Vol. , Issue 92g
[page]

1992
*
Mathematical Reviews
*

A hypergraph has property (S) if every minimal transversal is

*the*support of a stochastic function.*Sums*and products of hypergraphs are*defined**in*a*natural*way. ...*the**number*of edges*in**the**graph*.” ...##
###
Hodge Theory of Matroids

2017
*
Notices of the American Mathematical Society
*

If is

doi:10.1090/noti1463
fatcat:qe5ouzu5cbbgbp3zov6mk4a734
*the*set of edges of a*finite**graph*, call a subset of a flat when there is no edge*in*\ whose endpoints are connected by a path*in*. This*defines*a graphic matroid*on*. ... Write for a*finite*subset of a vector space and ( ) for*the**number*of*independent*subsets of of size . Example 3. ...##
###
Author index to volume 181 (1998)

1998
*
Discrete Mathematics
*

Schoen,

doi:10.1016/s0012-365x(97)82062-6
fatcat:sqdp43rjovam5az5gxnwxknhxq
*Independent**finite**sums**in**graphs**defined**on**the**natural**numbers*(Note) , A.N.,*On*k-weak orders: Recognition and a tolerance result (1-3) Tsai, Y.S., see H.J. Shyr (1-3) ... Ordaz, Neighborhood conditions for balanced*independent*sets*in*bipartite*graphs*(1 3 B6na, M., Permutations with*one*or two 132-subsequences (Note) (1 3 Bogart, K.P. and G. ...##
###
Page 1344 of Mathematical Reviews Vol. , Issue 85d
[page]

1985
*
Mathematical Reviews
*

*The*Ramsey

*number*r(m,n) is

*defined*to be

*the*smallest integer p such that every

*graph*of order p contains either a complete subgraph

*on*m vertices or a set of n

*independent*vertices. ...

*In*previous papers

*the*author has shown that many of

*the*spectral properties for

*finite*

*graphs*carry over to

*the*newly

*defined*infinite case [Publ. Inst. Math. ...

##
###
On the density of sets of the Euclidean plane avoiding distance 1
[article]

2021
*
arXiv
*
pre-print

*In*this paper we study

*the*

*number*m_1(ℝ^2) which is

*the*supremum of

*the*upper densities of measurable sets avoiding distance 1

*in*

*the*Euclidean plane. ... This parameter is related to

*the*fractional chromatic

*number*χ_f(ℝ^2) of

*the*plane. We establish that m_1(ℝ^2) ≤ 0.25647 and χ_f(ℝ^2) ≥ 3.8991. ...

*The*fractional chromatic

*number*of a

*graph*G (

*finite*or not), χ f (G), is then

*defined*as χ f (G) = inf b χ b (G) b . ...

##
###
Finite-Time and Fixed-Time Consensus of Multiagent Networks with Pinning Control and Noise Perturbation

2019
*
SIAM Journal on Applied Mathematics
*

Unlike

doi:10.1137/18m1174143
fatcat:hzarp2t2qrhl3dxmb7cpsubprq
*the**finite*-time control,*the*settling time of network systems with fixed-time control is*independent*of*the*... Our analysis will*naturally*lead to looking into how*the*settling time of*the*finitetime consensus depends*on**the*initial states of*the*system. ... Let i \*in*\scrV ; then*the**graph*p-Laplacian is*defined*as (3.1) (\Delta p \zeta ) i = \*sum*j\*in*\scrN i a ij \phi p (\zeta i -\zeta j ), where \zeta is a function*on*\scrV and \phi p : \BbbR \rightar ...##
###
Politopos en filogenética

2021
*
Tequio
*

to

doi:10.53331/teq.v4i11.0649
fatcat:gwl32d6xzjdhzn54u7vxho566a
*natural**numbers*. ...*The*Tight span and*the*Lipschitz polytope are both associated to*finite*metric spaces and can be connected to distance-preserving embeddings, while*the*balanced minimum evolution (BME) polytope is associated ...*The*minimum evolution polytope*on**the*other hand is associated to*natural**numbers*∈ ℕ nA .*In**the*following, we aim to introduce and motivate*the*main objects. ...##
###
Entropy and expansion
[article]

2020
*
arXiv
*
pre-print

*The*proof method yields inequalities for other measures of randomness, including covariance. As an application, we give upper bounds for

*independent*sets

*in*both

*finite*and infinite

*graphs*. ... We give another lower bound for

*the*same

*sum*

*in*terms of

*the*individual entropies when

*the*variables are functions of

*independent*random seeds. ... Bálint Virág was also supported by

*the*Canada Research Chair program,

*the*NSERC Discovery Accelerator grant, and

*the*ERC Consolidator Grant InvGroGra 648017. ...

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