# Combinatorics Seminar 2015

Date: Sat, Jun 13, 2015

Time: 09:45 - 10:45

Venue: Middle Meeting Room

Title: On tight spherical designs of harmonic index $t$ (or $T$)

Abstract:

Let $T$ be a finite subset of positive integers. A finite subset $Y$ of the $(n-1)$-sphere $\mathbb{S}^{n-1}$ is called a spherical design of harmonic index $T$, if $\sum_{\mathbf{x}\in Y}f(\mathbf{x})=0$ is satisfied for all homogeneous harmonic polynomials $f(x_1,\ldots,x_n)$ of degree $k\in T$.

This talk is about spherical designs of harmonic index $T$, including the special case of $T$ being a singleton set $\{t\}$. We give a Fisher type lower bound for the size of such a design and discuss the tightness of our bound.

This is joint work with Eiichi Bannai, Etsuko Bannai, Kyoung-Tark Kim and Wei-Hsuan Yu.

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