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math.CO2026
Self-complementary completions on six vertices
Xinan Dai, Wenhao Deng, Yingdong Shi +2
Let \(\cthreshold(n)\) be the largest integer \(q\) such that every loopless digraph on \(n\) vertices with at most \(q\) arcs is isomorphic to a spanning subdigraph of a self-comp…
math.CO2026
A Negative Answer to Stanley's Problem 4 on Differential Posets
Xinan Dai, Wenhao Deng, Yingdong Shi +2
In Problem 4 of his 1988 paper on differential posets, Stanley asked whether the weighted -multichain series of an arbitrary differential poset is always a rational multiple of…
math.CO2026
An Explicit Counterexample to Stanley's Rankwise Lower-Bound Conjecture for Differential Posets
Xinan Dai, Wenhao Deng, Yingdong Shi +2
In Problem 6 of his 1988 paper on differential posets, Stanley asked for the least possible cardinality of a fixed rank of an -differential poset and suggested that the minimum…