From the 1 of 8 linked papers with an AI index.
8 papers
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…
Centralizer Excess as an Obstruction to Carlson's Depth Conjecture
Xinan Dai, Kuok Fai Chao
The paper studies why Carlson's depth conjecture fails for the group G = SmallGroup(128,859) over the field 𝔽₂, introducing a centralizer‑excess criterion that links depth equalit…
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…