3 papers
math.NT2026
Geometric designs and Hilbert-Kamke equations of degree five for classical orthogonal polynomials
Teruyuki Mishima, Xiao-Nan Lu, Masanori Sawa +1
In this paper we elucidate the advantage of examining the connections between Hilbert-Kamke equations and geometric designs, or Chebyshev-type quadrature, for classical orthogonal…
math.CO2026
Combinatorial designs and the Prouhet--Tarry--Escott problem
Munenori Inagaki, Hideki Matsumura, Masanori Sawa +1
This is the first paper that provides a systematic treatment of the -dimensional PTE problem in additive number theory, abbreviated by PTE, through its connection with combi…
math.NT2025
On a group of normalized solutions of the higher-dimensional Prouhet--Tarry--Escott problem
Munenori Inagaki, Hideki Matsumura, Masanori Sawa +1
We elucidate, for the first time, a novel group-theoretic structure that arises from certain solutions of the -dimensional Prouhet--Tarry--Escott problem of degree and size…