Kada Williams

activity

20242026

collaborators

10 papers

math.CO2026

Inverting Dependently Random Tournaments

Kada Williams

Let $inv (T)$ be the inversion index of the tournament $T$ . Answering a question of Behague, we show that $inv (T_{1} \to T_{2}) = inv (T_{1}) + inv (T_{2})$ does not ev…

math.CO2026

Three-Layer Intersecting Temperate Families

Kada Williams

In response to a conjecture of Petr and Turek, we prove that every largest intersecting temperate collection of sets $\mathcal{A}\subseteq [2k]^{(k)}\cup [2k]^{(k+1)}\cup [2k]^{(k+…

math.CO2026

Confirmation of the Daykin-Frankl Conjecture

Kada Williams

In 1983, Daykin and Frankl conjectured that if $P$ is a convex subset of $Q_{n}$ , then it contains at least $∣ P ∣ (⌊ n /2 ⌋ n) 2^{- n}$ pairwise incomparable elements. W…

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 $∣ X ∣ = α 2^{n}$ , $∣ Y ∣ = β 2^{n}$ , the density of the set…

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

Fernández-Bretón, 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 are…

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…

math.CO2024

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.CO2024

The Width of a Ball in a Hypercube

Kada Williams

Various authors have calculated how many pairwise incomparable points can be selected from a partially ordered set. We tackle this question for the family of subsets of a finite se…