Hiroshi Nozaki

activity

20062025

most citedOn the zeros of Eisenstein series for

Γ_{0}^{*} (2)

and

Γ_{0}^{*} (3)

26 citations · 53 across the 32 of their papers we have counts for

collaborators

33 papers

math.CO2025

Pseudo-Euclidean representations of switching classes of Johnson and Hamming graphs with minimal dimension

Hiroshi Nozaki, Masashi Shinohara, Sho Suda

This paper considers minimum-dimensional representations of graphs in pseudo-Euclidean spaces, where adjacency and non-adjacency relations are reflected in fixed scalar square valu…

math.CO2023

Euclidean sets with only one distance modulo a prime ideal

Hiroshi Nozaki

Let $X$ be a finite set in the Euclidean space $R^{d}$ . If the squared distance between any two distinct points in $X$ is an odd integer, then the cardinality of $X$ is boun…

math.CO2023

Spherical designs and modular forms of the $D_{4}$ lattice

Masatake Hirao, Hiroshi Nozaki, Koji Tasaka

In this paper, we study shells of the $D_{4}$ lattice with a {slight generalization} of spherical $t$ -designs due to Delsarte-Goethals-Seidel, namely, the spherical design of harmoni…

math.CO2022

Embedding dimensions of matrices whose entries are indefinite distances in the pseudo-Euclidean space

Hiroshi Nozaki, Masashi Shinohara, Sho Suda

A finite set of the Euclidean space is called an $s$ -distance set provided the number of Euclidean distances in the set is $s$ . Determining the largest possible $s$ -distance set fo…

math.CO2022

Rationality of the inner products of spherical $s$ -distance $t$ -designs for $t \geq 2 s - 2$ , $s \geq 3$

Peter Boyvalenkov, Hiroshi Nozaki, Navid Safaei

We prove that the inner products of spherical $s$ -distance $t$ -designs with $t \geq 2 s - 2$ (Delsarte codes) and $s \geq 3$ are rational with the only exception being the icosahedron…

math.MG2022

Bounds for sets with few distances distinct modulo a prime ideal

Hiroshi Nozaki

Let $O_{K}$ be the ring of integers of an algebraic number field $K$ embedded into $C$ . Let $X$ be a subset of the Euclidean space $R^{d}$ , and $D (X)$ be th…

math.MG2020

A proof of a Dodecahedron conjecture for distance sets

Hiroshi Nozaki, Masashi Shinohara

A finite subset of a Euclidean space is called an $s$ -distance set if there exist exactly $s$ values of the Euclidean distances between two distinct points in the set. In this pape…

math.CO2020★ 3 cited

On the spectrum and linear programming bound for hypergraphs

Sebastian M. Cioabă, Jack H. Koolen, Masato Mimura +2

The spectrum of a graph is closely related to many graph parameters. In particular, the spectral gap of a regular graph which is the difference between its valency and second eigen…

math.CO2019

Maximal $2$ -distance sets containing the regular simplex

Hiroshi Nozaki, Masashi Shinohara

A finite subset $X$ of the Euclidean space is called an $m$ -distance set if the number of distances between two distinct points in $X$ is equal to $m$ . An $m$ -distance set $X$ is s…

math.CO2018★ 1 cited

A spectral version of the Moore problem for bipartite regular graphs

Sebastian M. Cioabă, Jack H. Koolen, Hiroshi Nozaki

Let $b (k, θ)$ be the maximum order of a connected bipartite $k$ -regular graph whose second largest eigenvalue is at most $θ$ . In this paper, we obtain a general upper bound for $b(k…

math.CO2017

Largest regular multigraphs with three distinct eigenvalues

Hiroshi Nozaki

We deal with connected $k$ -regular multigraphs of order $n$ that has only three distinct eigenvalues. In this paper, we study the largest possible number of vertices of such a grap…

math.CO2016

Maximal $m$ -distance sets containing the representation of the Hamming graph $H (n, m)$

Saori Adachi, Rina Hayashi, Hiroshi Nozaki +1

A set $X$ in the Euclidean space $R^{d}$ is called an $m$ -distance set if the set of Euclidean distances between two distinct points in $X$ has size $m$ . An $m$ -distance set…

math.CO2015

Complex spherical codes with three inner products

Hiroshi Nozaki, Sho Suda

Let $X$ be a finite set in a complex sphere of $d$ dimension. Let $D (X)$ be the set of usual inner products of two distinct vectors in $X$ . A set $X$ is called a complex spherical…

math.CO2015

On the largest subsets avoiding the diameter of $(0, \pm 1)$ -vectors

Saori Adachi, Hiroshi Nozaki

Let $L_{mk l} \subset R^{m + k + l}$ be the set of vectors which have $m$ of entries $- 1$ , $k$ of entries $0$ , and $l$ of entries $1$ . In this paper, we investigate the largest…

math.CO2015★ 1 cited

Maximizing the order of a regular graph of given valency and second eigenvalue

Sebastian M. Cioabă, Jack H. Koolen, Hiroshi Nozaki +1

From Alon and Boppana, and Serre, we know that for any given integer $k \geq 3$ and real number $λ < 2 k - 1$ , there are finitely many $k$ -regular graphs whose second largest eige…

math.CO2015

Complex spherical codes with two inner products

Hiroshi Nozaki, Sho Suda

A finite set $X$ in a complex sphere is called a complex spherical $2$ -code if the number of inner products between two distinct vectors in $X$ is equal to $2$ . In this paper, we c…

math.CO2014★ 2 cited

Linear programming bounds for regular graphs

Hiroshi Nozaki

Delsarte, Goethals, and Seidel (1977) used the linear programming method in order to find bounds for the size of spherical codes endowed with prescribed inner products between dist…

math.CO2013★ 2 cited

Weighing matrices and spherical codes

Hiroshi Nozaki, Sho Suda

Mutually unbiased weighing matrices (MUWM) are closely related to an antipodal spherical code with 4 angles. In the present paper, we clarify the relationship between MUWM and the…

math.CO2013

Polynomial properties on large symmetric association schemes

Hiroshi Nozaki

In this paper we characterize "large" regular graphs using certain entries in the projection matrices onto the eigenspaces of the graph. As a corollary of this result, we show that…

math.NA2012★ 1 cited

Remarks on Hilbert identities, isometric embeddings, and invariant cubature

Hiroshi Nozaki, Masanori Sawa

Victoir (2004) developed a method to construct cubature formulae with various combinatorial objects. Motivated by this, we generalize Victoir's method with one more combinatorial o…

math.CO2012

A characterization of skew Hadamard matrices and doubly regular tournaments

Hiroshi Nozaki, Sho Suda

We give a new characterization of skew Hadamard matrices of size $n$ in terms of the data of the spectra of tournaments of size $n - 2$ .

math.CO2011★ 1 cited

A spectral equivalent condition of the $P$ -polynomial property for association schemes

Hirotake Kurihara, Hiroshi Nozaki

We give an equivalent condition of the $P$ -polynomial property of symmetric association schemes.

math.NA2011

A new approach for the existence problem of minimal cubature formulas based on the Larman-Rogers-Seidel theorem

Masatake Hirao, Hiroshi Nozaki, Masanori Sawa +1

In this paper we consider the existence problem of cubature formulas of degree 4k+1 for spherically symmetric integrals for which the equality holds in the Möller lower bound. We p…

math.NA2011★ 6 cited

Note on cubature formulae and designs obtained from group orbits

Hiroshi Nozaki, Masanori Sawa

In 1960, Sobolev proved that for a finite reflection group G, a G-invariant cubature formula is of degree t if and only if it is exact for all G-invariant polynomials of degree at…

Pseudo-Euclidean representations of switching classes of Johnson and Hamming graphs with minimal dimension

Euclidean sets with only one distance modulo a prime ideal

Spherical designs and modular forms of the D4​ lattice

Embedding dimensions of matrices whose entries are indefinite distances in the pseudo-Euclidean space

Rationality of the inner products of spherical s-distance t-designs for t≥2s−2, s≥3

Bounds for sets with few distances distinct modulo a prime ideal

A proof of a Dodecahedron conjecture for distance sets

On the spectrum and linear programming bound for hypergraphs

Maximal 2-distance sets containing the regular simplex

A spectral version of the Moore problem for bipartite regular graphs

Largest regular multigraphs with three distinct eigenvalues

Maximal m-distance sets containing the representation of the Hamming graph H(n,m)

Complex spherical codes with three inner products

On the largest subsets avoiding the diameter of (0,±1)-vectors

Maximizing the order of a regular graph of given valency and second eigenvalue

Complex spherical codes with two inner products

Linear programming bounds for regular graphs

Weighing matrices and spherical codes

Polynomial properties on large symmetric association schemes

Remarks on Hilbert identities, isometric embeddings, and invariant cubature

A characterization of skew Hadamard matrices and doubly regular tournaments

A spectral equivalent condition of the P-polynomial property for association schemes

A new approach for the existence problem of minimal cubature formulas based on the Larman-Rogers-Seidel theorem

Note on cubature formulae and designs obtained from group orbits

Spherical designs and modular forms of the $D_{4}$ lattice

Rationality of the inner products of spherical $s$ -distance $t$ -designs for $t \geq 2 s - 2$ , $s \geq 3$

Maximal $2$ -distance sets containing the regular simplex

Maximal $m$ -distance sets containing the representation of the Hamming graph $H (n, m)$

On the largest subsets avoiding the diameter of $(0, \pm 1)$ -vectors

A spectral equivalent condition of the $P$ -polynomial property for association schemes