6 papers
Topological isomorphism of procountable groups is universal analytic
Xinan Dai, Wenhao Deng, Yingdong Shi +2
We prove that topological isomorphism of procountable groups is a universal analytic equivalence relation, answering a question of Gao, Nies, and Paolini. The same conclusion follo…
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…
The Minimum Cardinality of a Dependent Finite Gabor System Is Four
Xinan Dai, Wenhao Deng, Yingdong Shi +2
Recent work produced a linearly dependent system of twelve time--frequency shifts of a Schwartz function, disproving the HRT conjecture. We show that four shifts already suffice, a…
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…
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…
An Exact Counterexample to Carlson's Associated-Prime Depth Conjecture from a Group of Order 128
Xinan Dai, Wenhao Deng, Yingdong Shi +2
In Question~3.1 of his 1995 paper on depth and transfer, Carlson asked whether the depth of a finite-group cohomology ring is always realized by the dimension of one of its associa…