K. Nomoto

activity

20172020

collaborators

5 papers

math.CO2020

The critical number of $I_{1, t}$ -free triangle-free binary matroids

Peter Nelson, Kazuhiro Nomoto

A simple binary matroid, viewed as a restriction of a finite binary projective geometry $P G (n - 1, 2)$ , is $I_{1, t}$ -free if for any rank- $t$ flat of $P G (n - 1, 2)$ , its intersection wit…

math.CO2020

The smallest $I_{5}$ -free and triangle-free binary matroids

Peter Nelson, Kazuhiro Nomoto

We determine the smallest simple triangle-free binary matroids that have no five-element independent flat. This solves a special case of a conjecture of Nelson and Norin.

math.CO2020

The structure of $I_{4}$ -free and triangle-free binary matroids

Peter Nelson, Kazuhiro Nomoto

A simple binary matroid is called $I_{4}$ -free if none of its rank-4 flats are independent sets. These objects can be equivalently defined as the sets $E$ of points in $P G (n - 1, 2)$ fo…

math.CO2018

The structure of claw-free binary matroids

Peter Nelson, Kazuhiro Nomoto

A simple binary matroid is called claw-free if none of its rank-3 flats are independent sets. These objects can be equivalently defined as the sets $E$ of points in $\mathrm{PG}(n-…

math.CO2017

Stability and exact Turan numbers for matroids

Hong Liu, Sammy Luo, Peter Nelson +1

We consider the Turán-type problem of bounding the size of a set $M \subseteq F_{2}^{n}$ that does not contain a linear copy of a given fixed set $N \subseteq F_{2}^{k}$ ,…

The critical number of I1,t​-free triangle-free binary matroids

The smallest I5​-free and triangle-free binary matroids

The structure of I4​-free and triangle-free binary matroids

The structure of claw-free binary matroids

Stability and exact Turan numbers for matroids

The critical number of $I_{1, t}$ -free triangle-free binary matroids

The smallest $I_{5}$ -free and triangle-free binary matroids

The structure of $I_{4}$ -free and triangle-free binary matroids