Kada Williams

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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…