T. Luczak

activity

19932023

most citedUnmodulated spin chains as universal quantum wires

241 citations · 498 across the 19 of their papers we have counts for

collaborators

Showing 2017Show all

4 papers · 1 filter

math.CO2017★ 1 cited

A tale of stars and cliques

Tomasz Łuczak, Joanna Polcyn, Christian Reiher

We show that for an infinitely many natural numbers $k$ there are $k$ -uniform hypergraphs which admit a `rescaling phenomenon' as described in [9]. More precisely, let $\mathcal{A}…

math.CO2017★ 1 cited

The multipartite Ramsey number for the 3-path of length three

Tomasz Luczak, Joanna Polcyn

We study the Ramsey number for the 3-path of length three and $n$ colors and show that $R (P_{3}^{3}; n) \leq λ_{0} n + 7 n$ , for some explicit constant $λ_{0} = 1.97466 \dots$ .

math.CO2017★ 2 cited

Paths in hypergraphs: a rescaling phenomenon

Tomasz Luczak, Joanna Polcyn

Let $P_{ℓ}^{k}$ denote the loose $k$ -path of length $ℓ$ and let define $f_{ℓ}^{k} (n, m)$ as the minimum value of $Δ (H)$ over all $P_{ℓ}^{k}$ -free $k$ -graphs $H$ with $n$ vertices an…

math.CO2017

On multicolor Ramsey numbers for loose $k$ -paths of length three

Tomasz Łuczak, Joanna Polcyn, Andrzej Ruciński

We show that there exists an absolute constant $A$ such that for each $k \geq 2$ and every coloring of the edges of the complete $k$ -uniform hypergraph on $A r$ vertices with $r$ colo…

A tale of stars and cliques

The multipartite Ramsey number for the 3-path of length three

Paths in hypergraphs: a rescaling phenomenon

On multicolor Ramsey numbers for loose k-paths of length three

On multicolor Ramsey numbers for loose $k$ -paths of length three