ZZZijian Zeng
Zijian Zeng
*This is an algorithmically generated author record based on publicly available information.
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The organizations/institutes from the scholar's latest article
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Zijian Zeng has a total of 3 co-authors. Here are the top co-authors by number of shared publications:
- Houde Liu
Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China
1 shared publication - Kurunathan Ratnavelu
UCSI University, Malaysia
1 shared publication - Seng Huat Ong
Institute of Mathematical Sciences, University of Malaya
1 shared publication
Latest Publications
- Open Access
- 24 August 2026
- Published by MDPI AG in Preprints.org
Exact Finite Certificates for the Four-Dimensional Ternary Borsuk Problem and Five-Dimensional Ternary Kissing Codes
We determine two finite models motivated by open problems in discrete geometry. Let $T_4=\{-1,0,1\}^4$. We prove that the maximum Borsuk number of a subset of $T_4$ is exactly 4: every nondegenerate subset can be partitioned into four sets of strictly smaller diameter, and a four-point equidistant set shows sharpness. Let $U_5=\{v/\lVert v\rVert:v\in\{-1,0,1\}^5\setminus\{0\}\}$. We also prove that a spherical code in $U_5$ with pairwise inner products at most $1/2$ has at most 40 points, with equality only for the $D_5$ root system inside this fixed library. The first result is certified by exact distance-layer colorings and an exhaustive symmetry-reduced enumeration of 15,056 maximal feasible sets; the second by two exact maximum-clique computations using integer predicates. These are finite-library theorems: they do not settle Borsuk's conjecture in $R^4$ or the unrestricted kissing numbers in dimensions 5 and 6.- 24 August 2026
- Published by MDPI AG in Preprints.org
Open AccessExact Finite Certificates for the Four-Dimensional Ternary Borsuk Problem and Five-Dimensional Ternary Kissing Codes
We determine two finite models motivated by open problems in discrete geometry. Let $T_4=\{-1,0,1\}^4$. We prove that the maximum Borsuk number of a subset of $T_4$ is exactly 4: every nondegenerate subset can be partitioned into four sets of strictly smaller diameter, and a four-point equidistant set shows sharpness. Let $U_5=\{v/\lVert v\rVert:v\in\{-1,0,1\}^5\setminus\{0\}\}$. We also prove that a spherical code in $U_5$ with pairwise inner products at most $1/2$ has at most 40 points, with equality only for the $D_5$ root system inside this fixed library. The first result is certified by exact distance-layer colorings and an exhaustive symmetry-reduced enumeration of 15,056 maximal feasible sets; the second by two exact maximum-clique computations using integer predicates. These are finite-library theorems: they do not settle Borsuk's conjecture in $R^4$ or the unrestricted kissing numbers in dimensions 5 and 6.