Paul A. Russell

activity

20062026

most citedThe Group Evolution Multiwavelength Study (GEMS): The near-infrared luminosity function of nearby galaxy groups

19 citations · 41 across the 9 of their papers we have counts for

collaborators

Showing math.COShow all

8 papers · 1 filter

math.CO2018

Inhomogeneous Partition Regularity

Imre Leader, Paul A. Russell

We say that the system of equations $A x = b$ , where $A$ is an integer matrix and $b$ is a (non-zero) integer vector, is partition regular if whenever the integers are finitely colour…

math.CO2017

Monochromatic infinite sumsets

Imre Leader, Paul A. Russell

We show that there is a rational vector space $V$ such that, whenever $V$ is finitely coloured, there is an infinite set $X$ whose sumset $X + X$ is monochromatic. Our example is the…

math.CO2013★ 1 cited

Set Systems Containing Many Maximal Chains

J. Robert Johnson, Imre Leader, Paul A. Russell

The purpose of this short problem paper is to raise an extremal question on set systems which seems to be natural and appealing. Our question is: which set systems of a given size…

math.CO2011

Probably Intersecting Families are Not Nested

Paul A. Russell, Mark Walters

It is well known that an intersecting family of subsets of an n-element set can contain at most 2^(n-1) sets. It is natural to wonder how `close' to intersecting a family of size g…

math.CO2011★ 2 cited

Compressions and Probably Intersecting Families

Paul A. Russell

A family X of sets is said to be intersecting if any two members of X have non-empty intersection. It is a well-known and simple fact that an intersecting family of subsets of [n]=…

math.CO2010

Transitive Sets and Cyclic Quadrilaterals

Imre Leader, Paul A. Russell, Mark Walters

Motivated by some questions in Euclidean Ramsey theory, our aim in this note is to show that there exists a cyclic quadrilateral that does not embed into any transitive set (in any…

math.CO2010★ 1 cited

Transitive Sets in Euclidean Ramsey Theory

Imre Leader, Paul A. Russell, Mark Walters

A finite set $X$ in some Euclidean space $R^{n}$ is called Ramsey if for any $k$ there is a $d$ such that whenever $R^{d}$ is $k$ -coloured it contains a monochromatic set congruent to…

math.CO2007

Families intersecting on an interval

Paul A. Russell

We shall be interested in the following Erdos-Ko-Rado-type question. Fix some subset B of [n]. How large a family A of subsets of [n] can we find such that the intersection of any…