N. Tokushige

activity

20102026

most citedA semidefinite programming approach to a cross-intersection problem with measures

7 citations · 17 across the 20 of their papers we have counts for

collaborators

21 papers

math.CO2026

A product inequality and its application to cross-intersecting families

Toshihiro Shimizu, Norihide Tokushige

For an integer $r \geq 3$ and real numbers $a_{1}, \dots, a_{r} \in (0, 1)$ , let $a = a_{1} \dots a_{r}$ . We show that \[ \prod_{i=1}^r(a_i+a_i^2+\cdots+a_i^r)\geq \prod_{i=1}^r(a_i+a_i^2+\cdots+…

math.CO2026

A product theorem for $r$ -cross intersecting families of subspaces

Toshihiro Shimizu, Norihide Tokushige

Let $V$ be an $n$ -dimensional vector space over a finite field of order $q$ . Let $r \geq 3$ , $(r - 1) n \geq r k$ and let $\mathcal F_1,\ldots,\mathcal F_r\subset \genfrac{[}{]}{0pt}{}{V…

math.CO2025

Burning numbers via eigenpolytopes -- Hamming graphs, Johnson graphs, and halved cubes

Hajime Tanaka, Norihide Tokushige

We give lower and upper bounds on the burning number of Hamming graphs, Johnson graphs, and halved cube graphs. For the lower bounds, we use the fact that $1$ -skeletons of the eige…

math.CO2025

A semidefinite programming approach to cross $2$ -intersecting families

Hajime Tanaka, Norihide Tokushige

Let $k \geq 2$ and $n \geq 3 (k - 1)$ . Let $F$ and $G$ be families of $k$ -element subsets of an $n$ -element set. Suppose that $∣ F \cap G ∣ \geq 2$ for all $F\in\mathcal…

math.CO2024

Alon's transmitting problem and multicolor Beck--Spencer Lemma

Norihide Tokushige

The Hamming graph $H (n, q)$ is defined on the vertex set ${1, 2, \dots, q}^{n}$ and two vertices are adjacent if and only if they differ in precisely one coordinate. Alon (1992) prove…

math.CO2024

Burning Hamming graphs

Norihide Tokushige

The Hamming graph $H (n, q)$ is defined on the vertex set $[q]^{n}$ and two vertices are adjacent if and only if they differ in precisely one coordinate. Alon \cite{Alon} proved that t…

math.CO2024

Extremal problems for intersecting families of subspaces with a measure

Hajime Tanaka, Norihide Tokushige

We introduce a measure for subspaces of a vector space over a $q$ -element field, and propose some extremal problems for intersecting families. These are $q$ -analogue of Erdős-Ko-Ra…

math.CO2023

Strong stability of 3-wise $t$ -intersecting families

Norihide Tokushige

Let $G$ be a family of subsets of an $n$ -element set. The family $G$ is called $3$ -wise $t$ -intersecting if the intersection of any three subsets in ${\mathca…

math.CO2022

Non-trivial 3-wise intersecting uniform families

Norihide Tokushige

A family of $k$ -element subsets of an $n$ -element set is called 3-wise intersecting if any three members in the family have non-empty intersection. We determine the maximum size of…

math.CO2022

Counting cliques in a random graph

Taro Sakurai, Norihide Tokushige

We show that the expected number of cliques in the Erdős-Rényi random graph $G (n, p)$ is $n^{\frac{1}{- 2 l o g p} (l o g n - 2 l o g l o g n + O (1))}$ .

math.CO2022

The maximum measure of non-trivial 3-wise intersecting families

Norihide Tokushige

Let $G$ be a family of subsets of an $n$ -element set. The family $G$ is called non-trivial $3$ -wise intersecting if the intersection of any three subsets in $\mat…

math.CO2021

Application of hypergraph Hoffman's bound to intersecting families

Norihide Tokushige

Using the Filmus-Golubev-Lifshitz method to bound the independence number of a hypergraph, we solve some problems concerning multiply intersecting families with biased measure. Amo…

math.CO2021★ 2 cited

The maximum measure of 3-wise t-intersecting families

Norihide Tokushige

Let $G$ be a family of subsets of an $n$ -element set. The family $G$ is called $3$ -wise $t$ -intersecting if the intersection of any three subsets in $G$ …

math.CO2019★ 4 cited

Avoiding a shape, and the slice rank method for a system of equations

Masato Mimura, Norihide Tokushige

Fix a vector space over a finite field and a system of linear equations. We provide estimates, in terms of the dimension of the vector space, of the maximum of the sizes of subsets…

math.CO2019★ 1 cited

Avoiding a star of three-term arthmetic progressions

Masato Mimura, Norihide Tokushige

We provide an upper bound of the size of a subset A of F_p^n that does not admit a k-star of 3-APs (three-term arithmetic progressions). Namely, the subset A is assumed to contain…

math.CO2018

When are stars the largest cross intersecting families?

Norihide Tokushige

We provide a necessary and sufficient condition for stars to be the largest cross intersecting families.

math.CO2018★ 2 cited

AK-type stability theorems on cross t-intersecting families

Sang June Lee, Mark Siggers, Norihide Tokushige

Two families, $A$ and $B$ , of subsets of $[n]$ are cross $t$ -intersecting if for every $A \in A$ and $B \in B$ , $A$ and $B$ intersect in…

math.CO2015

Multiply union families in $N^{n}$

Peter Frankl, Masashi Shinohara, Norihide Tokushige

Let $A \subset N^{n}$ be an $r$ -wise $s$ -union family, that is, a family of sequences with $n$ components of non-negative integers such that for any $r$ sequences in $A$ th…

math.CO2015

Towards extending the Ahlswede-Khachatrian theorem to cross t-intersecting families

Sang June Lee, Mark Siggers, Norihide Tokushige

Ahlswede and Khachatrian's diametric theorem is a weighted version of their complete intersection theorem, itself an extension of the $t$ -intersecting Erdős-Ko-Rado theorem. Their…

math.CO2015★ 7 cited

A semidefinite programming approach to a cross-intersection problem with measures

Sho Suda, Hajime Tanaka, Norihide Tokushige

We present a semidefinite programming approach to bound the measures of cross-independent pairs in a bipartite graph. This can be viewed as a far-reaching extension of Hoffman's ra…

math.CO2010★ 1 cited

Application of arrangement theory to unfolding models

Hidehiko Kamiya, Akimichi Takemura, Norihide Tokushige

Arrangement theory plays an essential role in the study of the unfolding model used in many fields. This paper describes how arrangement theory can be usefully employed in solving…

A product inequality and its application to cross-intersecting families

A product theorem for r-cross intersecting families of subspaces

Burning numbers via eigenpolytopes -- Hamming graphs, Johnson graphs, and halved cubes

A semidefinite programming approach to cross 2-intersecting families

Alon's transmitting problem and multicolor Beck--Spencer Lemma

Burning Hamming graphs

Extremal problems for intersecting families of subspaces with a measure

Strong stability of 3-wise t-intersecting families

Non-trivial 3-wise intersecting uniform families

Counting cliques in a random graph

The maximum measure of non-trivial 3-wise intersecting families

Application of hypergraph Hoffman's bound to intersecting families

The maximum measure of 3-wise t-intersecting families

Avoiding a shape, and the slice rank method for a system of equations

Avoiding a star of three-term arthmetic progressions

When are stars the largest cross intersecting families?

AK-type stability theorems on cross t-intersecting families

Multiply union families in Nn

Towards extending the Ahlswede-Khachatrian theorem to cross t-intersecting families

A semidefinite programming approach to a cross-intersection problem with measures

Application of arrangement theory to unfolding models

A product theorem for $r$ -cross intersecting families of subspaces

A semidefinite programming approach to cross $2$ -intersecting families

Strong stability of 3-wise $t$ -intersecting families

Multiply union families in $N^{n}$