64 citations · 124 across the 14 of their papers we have counts for
15 papers
Post-selection-free preparation of high-quality physical qubits
Ben Barber, Neil I. Gillespie, J. M. Taylor
Rapidly improving gate fidelities for coherent operations mean that errors in state preparation and measurement (SPAM) may become a dominant source of error for fault-tolerant oper…
Small sums of five roots of unity
Ben Barber
Motivated by questions in number theory, Myerson asked how small the sum of 5 complex nth roots of unity can be. We obtain a uniform bound of O(n^{-4/3}) by perturbing the vertices…
The Namer-Claimer game
Ben Barber
In each round of the Namer-Claimer game, Namer names a distance d, then Claimer claims a subset of [n] that does not contain two points that differ by d. Claimer wins once they hav…
Minimalist designs
Ben Barber, Stefan Glock, Daniela Kühn +3
The iterative absorption method has recently led to major progress in the area of (hyper-)graph decompositions. Amongst other results, a new proof of the Existence conjecture for c…
Isoperimetry in integer lattices
Ben Barber, Joshua Erde
The edge isoperimetric problem for a graph is to determine, for each , the minimum number of edges leaving any set of vertices. In general this problem is NP-hard, but e…
Clique decompositions of multipartite graphs and completion of Latin squares
Ben Barber, Daniela Kühn, Allan Lo +2
Our main result essentially reduces the problem of finding an edge-decomposition of a balanced r-partite graph of large minimum degree into r-cliques to the problem of finding a fr…
Fractional Clique Decompositions of Dense Graphs and Hypergraphs
Ben Barber, Daniela Kühn, Allan Lo +2
Our main result is that every graph on vertices with minimum degree has a fractional -decomposition. Combining this res…
Edge-decompositions of graphs with high minimum degree
Ben Barber, Daniela Kühn, Allan Lo +1
A fundamental theorem of Wilson states that, for every graph , every sufficiently large -divisible clique has an -decomposition. Here a graph is -divisible if $e(F)…
Distinguishing subgroups of the rationals by their Ramsey properties
Ben Barber, Neil Hindman, Imre Leader +1
A system of linear equations with integer coefficients is partition regular over a subset S of the reals if, whenever S\{0} is finitely coloured, there is a solution to the system…
Partition regularity without the columns property
Ben Barber, Neil Hindman, Imre Leader +1
A finite or infinite matrix A with rational entries is called partition regular if whenever the natural numbers are finitely coloured there is a monochromatic vector x with Ax=0. M…
Partition regularity of a system of De and Hindman
Ben Barber
We prove that a certain matrix, which is not image partition regular over R near zero, is image partition regular over N. This answers a question of De and Hindman.
Partition regularity with congruence conditions
Ben Barber, Imre Leader
An infinite integer matrix A is called image partition regular if, whenever the natural numbers are finitely coloured, there is an integer vector x such that Ax is monochromatic. G…
Partition regularity in the rationals
Ben Barber, Neil Hindman, Imre Leader
A system of homogeneous linear equations with integer coefficients is partition regular if, whenever the natural numbers are finitely coloured, the system has a monochromatic solut…
Random walks on quasirandom graphs
Ben Barber, Eoin Long
Let G be a quasirandom graph on n vertices, and let W be a random walk on G of length alpha n^2. Must the set of edges traversed by W form a quasirandom graph? This question was as…
Maximum hitting for n sufficiently large
Ben Barber
For a left-compressed intersecting family \A contained in [n]^(r) and a set X contained in [n], let \A(X) = {A in \A : A intersect X is non-empty}. Borg asked: for which X is |\A(X…