13 papers
A Proof of the Dittert Conjecture via Boundary Rigidity
Xinan Dai, Wenhao Deng, Yingdong Shi +2
Let be the simplex of nonnegative matrices whose entries sum to . For in , with row sums and column sums $c_1,\l…
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…
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 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.…
Centralizer Excess as an Obstruction to Carlson's Depth Conjecture
Xinan Dai, Kuok Fai Chao
Let and . The cohomology ring has depth two, and we prove that the minimum quotient dimension of an associated pri…
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…
L-packet multiplicity and integral structure in the K-theory of real inner forms
Xinan Dai, Kuok Fai Chao
Let be a connected linear real semisimple group with finite centre and discrete series, and let be a fixed compact inner form. We isolate an integral structure behind the…
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…