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Ziqing Xiang
I am an Associate Professor in the Department of Mathematics and National Center for Applied Mathematics Shenzhen, Southern University of Science and Technology.
Algebraic Combinatorics
- Classification of tight \(2s\)-designs with \(s \geq 2\). (PDF)
Supplemental material: codes and output
- On the two-distance embedding in real Euclidean space of coherent configuration of type \((2,2;3)\), joint work Eiichi Bannai, Etsuko Bannai, Chin-Yen Lee and Wei-Hsuan Yu.
- Explicit spherical designs.
(PDF)
Algebraic Combinatorics 5(2), 347-369, 2022. doi:10.5802/alco.213
- Classification of spherical \(2\)-distance \(\{4, 2, 1\}\)-designs by solving Diophantine equations, joint work Eiichi Bannai, Etsuko Bannai, Wei-Hsuan Yu and Yan Zhu.
(PDF)
Taiwanese Journal of Mathematics, 25, 1-22, 2021. doi:10.11650/tjm/200601
Supplemental material: code
(Mathematica Notebook)
(PDF)
- Rational designs, joint work with Zhen Cui and Jiacheng Xia.
(PDF)
Advances in Mathematics, 352, 541-571, 2019.
doi:10.1016/j.aim.2019.06.012
- Nonexistence of nontrivial tight \(8\)-designs.
(PDF)
Journal of Algebraic Combinatorics, 47(2), 301-318, 2018.
doi:10.1007/s10801-017-0776-0
- A Fisher type inequality for weighted regular \(t\)-wise balanced designs.
(PDF)
Journal of Combinatorial Theory A, 119(7), 1523-1527, 2012.
doi:10.1016/j.jcta.2012.04.008
Graph Theory
Number Theory
Representation Theory
- Quantum wreath products and Schur-Weyl duality I, joint work with Chun-Ju Lai and Daniel Nakano.
- Chapter 4 of “Introduction to Soergel bimodules” by Ben Elias, Shotaro Makisumi, Ulrich Thiel, Geordie Williamson,
RSME Springer Series 5, 2020. doi:10.1007/978-3-030-48826-0
- \(q\)-Schur algebras corresponding to Hecke algebras of type B, joint work with Chun-Ju Lai and Daniel Nakano.
(PDF)
Transformation Groups 27, 983-1024, 2022. doi:10.1007/s00031-020-09628-7
- Support varieties for Hecke algebras, joint work with Daniel Nakano.
(PDF)
Homology, Homotopy and Applications, 21(2), 59-82, 2019. doi:10.4310/HHA.2019.v21.n2.a5
Papers in preparation
- Majorana representation of complex vectors, Temperley-Lieb category, and two variable hypergeometric series, joint work with Shaoshi Chen, Mikio Nakahara, Yan Zhu.
- Finiteness of tight combinatorial designs.
- New lower bound on the sizes of designs. (abstract)
- Hamiltonian thickness and spanning topological minors, joint work with Yaokun Wu and Yinfeng Zhu. (abstract)
- Lit-only \(\sigma\)-game, joint work with Yaokun Wu. (abstract)
- Inferring phylogenies from incomplete metric information, joint work with Yaokun Wu, Zeying Xu, Yinfeng Zhu.
- Positive matrices, primitive matrices, scrambling matrices and contractible matrices, joint work with Xinmao Wang and Yaokun Wu.
- Fiber products of P-polynomial association schemes. (abstract)
- On \(s\)-distance sets in real hyperbolic space.
- Hyperbolicity of the product graphs.
Research Interests
- Combinatorics: association schemes, design theory, graph theory, symbolic dynamics, phylogenetic combinatorics.
- Number Theory: Diophantine equation, finiteness of integral points, variable separated curves.
- Representation Theory: algebraic groups, cohomology, Iwahori-Hecke algebras, quantum groups, Schur algebras.