Yan Zhu

activity

20152026

most citedOn the explicit constructions of certain unitary

t

-designs

11 citations · 19 across the 9 of their papers we have counts for

collaborators

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8 papers · 1 filter

math.CO2026

Trivariate $P$ - and $Q$ -polynomial structures for interior shells of the Grassmann scheme

Yan Zhu

Association schemes induced on the shells of the Grassmann scheme $G r_{q} (N, a)$ form an important family in the study of multivariate $P$ - and $Q$ -polynomial structures. For $a < N /2$ ,…

math.CO2026

$P$ -polynomial coherent configurations

Eiichi Bannai, Sho Suda, Yan Zhu

Suda introduced the notion of a $Q$ -polynomial coherent configuration, which provides a natural and important concept. Subsequently, Lato introduced a notion of a $P$ -polynomial co…

math.CO2024

Bivariate $Q$ -polynomial structures for the nonbinary Johnson scheme and the association scheme obtained from attenuated spaces

Eiichi Bannai, Hirotake Kurihara, Da Zhao +1

The study of $P$ -polynomial association schemes (distance-regular graphs) and $Q$ -polynomial association schemes, and in particular $P$ - and $Q$ -polynomial association schemes, has…

math.CO2023★ 3 cited

Multivariate P- and/or Q-polynomial association schemes

Eiichi Bannai, Hirotake Kurihara, Da Zhao +1

The classification problem of $P$ - and $Q$ -polynomial association schemes has been one of the central problems in algebraic combinatorics. Generalizing the concept of $P$ - and $Q$ -…

math.CO2020★ 1 cited

Tight relative $t$ -designs on two shells in hypercubes, and Hahn and Hermite polynomials

Eiichi Bannai, Etsuko Bannai, Hajime Tanaka +1

Relative $t$ -designs in the $n$ -dimensional hypercube $Q_{n}$ are equivalent to weighted regular $t$ -wise balanced designs, which generalize combinatorial $t$ - $(n, k, λ)$ des…

math.CO2017

Half of an antipodal spherical design

Eiichi Bannai, Da Zhao, Lin Zhu +2

We investigate several antipodal spherical designs on whether we can choose half of the points, one from each antipodal pair, such that they are balanced at the origin. In particul…

math.CO2015

Relative t-designs in binary Hamming association scheme H(n,2)

Eiichi Bannai, Etsuko Bannai, Yan Zhu

A relative t-design in the binary Hamming association schemes H(n,2) is equivalent to a weighted regular t-wise balanced design, i.e., certain combinatorial t-design which allow di…

math.CO2015★ 4 cited

More on spherical designs of harmonic index $t$

Yan Zhu, Eiichi Bannai, Etsuko Bannai +2

A finite subset $Y$ on the unit sphere $S^{n - 1} \subseteq R^{n}$ is called a spherical design of harmonic index $t$ , if the following condition is satisfied: $\sum_{\mathbf{…

Trivariate P- and Q-polynomial structures for interior shells of the Grassmann scheme

P-polynomial coherent configurations

Bivariate Q-polynomial structures for the nonbinary Johnson scheme and the association scheme obtained from attenuated spaces