Kada Williams

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20242026

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3 papers · 2 filters

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…