Kada Williams

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20242026

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7 papers · 1 filter

math.CO2026

Torus Queen Independence

Kada Williams

Define a queen on $Z_{n}^{d}$ with admissible moves parallel to $x \in {- 1, 0, 1}^{d}$ , of arbitrary length. How many queens can be placed on $Z_{n}^{d}$ without any…

math.CO2025

Greedy Gossiping

Kada Williams

The renowned Gossiping Problem (1971) asks the following. There are $n$ people who each know an item of gossip. In a telephone call, two people share all the gossip they know. How…

math.CO2025

A Correlation Inequality on Three Functions

Kada Williams

Let $X$ and $Y$ be upward closed set systems in the lattice of ${0, 1}^{n}$ . The celebrated Harris-Kleitman inequality implies that if $∣ X ∣ = I^\pm 2^{n}$ , $∣ Y ∣ = I^^{2} 2^{n}$ , the density of the s…

math.CO2024

The Width of Hamming Balls

Kada Williams

The width of a poset is the size of its largest antichain. Sperner's theorem states that $(2^{[n]}, \subset)$ is a poset whose width equals the size of its largest layer. We show th…

math.CO2024

Monochromatic Sumsets in Countable Colourings of Abelian Groups

Imre Leader, Kada Williams

FernÃ¡ndez-BretÃ³n, Sarmiento and Vera showed that whenever a direct sum of sufficiently many copies of $Z_{4}$ , the cyclic group of order 4, is countably coloured there ar…

math.CO2024

Layered subgraphs of the hypercube

Natalie Behague, Imre Leader, Natasha Morrison +1

A subgraph of the $n$ -dimensional hypercube is called 'layered' if it is a subgraph of a layer of some hypercube. In this paper we show that there exist subgraphs of the cube of ar…