Masanori Sawa

collaborators

3 papers

math.CO2025

Algebro-combinatorial generalizations of the Victoir method for constructing weighted designs

Hiroshi Nozaki, Masanori Sawa

A weighted $t$ -design in $R^{d}$ is a finite weighted set that exactly integrates all polynomials of degree at most $t$ with respect to a given probability measure. A fundam…

math.CO2025

Ellipsoidal designs and the Prouhet--Tarry--Escott problem

Hideki Matsumura, Masanori Sawa

The notion of ellipsoidal design was first introduced by Pandey (2022) as a full generalization of spherical designs on the unit circle $S^{1}$ . In this paper, we elucidate the advan…

math.CO2024

Antipodality of spherical designs with odd harmonic indices

Ryutaro Misawa, Akihiro Munemasa, Masanori Sawa

We determine the smallest size of a non-antipodal spherical design with harmonic indices ${1, 3, \dots, 2 m - 1}$ to be $2 m + 1$ , where $m$ is a positive integer. This is achieved by pro…