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math.CO2026

The least non-partitionable zero-sum subset for zero-sum triples in finite abelian groups

Yutong Zhang, Yaoran Yang

Let \(G\) be a finite abelian group, and let \(μ(G)\) denote the least size of a subset \(S\subseteq G\) with \(3\mid |S|\), total sum zero, and no partition into zero-sum triples…

math.CO2026

Betti Numbers of Cut Complexes of Squared Paths and a Recurrence Conjecture

Yutong Zhang, Yaoran Yang

For a graph on , the -cut complex has facets , where ranges over the -subsets that induce disconnected subgraphs of . Bayer, Denker,…

math.CO2026

Excess Obstructions and Layer-Contained Certificates for the Hypergraph Nash--Williams--Tutte Conjecture

Yutong Zhang, Yaoran Yang

Guo, Li, Shangguan, Tamo, and Wootters proposed a hypergraph analogue of the Nash--Williams--Tutte theorem, asserting that every -weakly-partition-connected hypergraph admits a…

math.CO2026

Rational Weyl group elements of odd type D

Yutong Zhang, Yaoran Yang

Voloshyn introduced rational Weyl group elements in connection with rational normal forms on complex reductive groups and conjectured that their number in type , for odd ,…