9 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…
The Borel complexity of conjugacy for Cantor minimal systems
Xinan Dai, Wenhao Deng, Yingdong Shi +2
We prove that conjugacy of minimal homeomorphisms of the Cantor space is Borel bireducible with isomorphism of countable graphs, answering the Cantor minimal case of a question of…
The Complex Banach Isometric Conjecture
Xinan Dai, Wendao Deng, Yidong Shi +2
Banach asked whether a normed space must be Hilbert if, for one fixed dimension greater than one, all subspaces of that dimension are linearly isometric. We prove the complex case.…
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…
Bounded Representatives in Critical Sobolev-Hodge Spaces
Xinan Dai, Wenhao Deng, Yidong Shi +2
Let , , and . We prove that every has a representative with $…
A Finite E-Group of Nilpotency Class Three
Xinan Dai, Wenhao Deng, Yidong Shi +2
A group is an E-group if every element commutes with each of its endomorphic images. Caranti asked whether a finite E-group can have nilpotency class three. We prove that the -g…
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…