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Supersaturation for Eventown via Generator Switching
Zicheng Han, Xiande Zhang, Yuhao Zhao
An eventown family is a family of even-sized subsets of in which every two distinct members have an even-sized intersection. A classical theorem of Berlekamp and Graver shows…
Bounds and constructions for constant/low-power error-correcting cooling codes
Shuangqing Liu, Tingting Tong, Menglong Zhang +2
The low-power error-correcting cooling (LPECC) codes and constant-power error-correcting cooling (CPECC) codes, introduced in [IEEE Trans. Inf. Theory, 64 (2018), 3062--3085; 66 (2…
A superlogarithmic saving for Oddtown modulo composite numbers
Yuhao Zhao
Let be the largest size of a family such that no member has size divisible by , while the intersection of every two distinct membe…
Lower bounds on the strength of the determinant
Qiyuan Chen, Yuhao Zhao
We establish new lower bounds for the strength and partition rank of the determinant. For every prime , we prove the exact identity \[ \operatorname{str}(\mathrm{det}_p)=p. \] A…