Patrick White

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math.CO2026

Tuza's Ryser-conjecture claim for four-partite hypergraphs with matching number two

Patrick White

We prove that every $4$ -partite $4$ -uniform hypergraph $H$ with matching number $ν (H) = 2$ satisfies $τ (H) \leq 6$ , where $τ$ denotes the vertex-cover number. This confirms a claim mad…

math.CO2026

The small Davenport constant of the Heisenberg group of order 125

Patrick White

The small Davenport constant $d (G)$ of a finite group $G$ is the maximal length of a product-one-free sequence over $G$ . For the exponent- $p$ Heisenberg group $H_{p^{3}}$ of…

math.CO2026

New bounds for double covers of the discrete box {0,1,2}^d

Patrick White

A proper sub-box of $A = {0, 1, 2}^{d}$ is a product $S_{1} \times \dots \times S_{d}$ with each $\emptyset \neq = S_{i} ⊊ {0, 1, 2}$ . A double cover is a finite multiset of proper sub-bo…