5 papers
The Vámos Matroid Has No Second Symmetric Power
Yasuhito Nakajima
Symmetric powers of matroids were introduced by Lovász and Mason. The subject has recently attracted renewed interest through its connection with the realizability of tropical line…
Decompositions of good involutions on quandles
Yasuhito Nakajima, Kentaro Yamaguchi
We study the behavior of good involutions under two fundamental constructions of quandles: interaction-free unions and direct products. In particular, we show that the set of good…
On the nonexistence of good involutions of symplectic quandles
Yasuhito Nakajima, Kentaro Yamaguchi
We investigate the necessary and sufficient condition for the existence of good involutions of symplectic quandles, which are defined on free -modules with an antisymmetric bili…
A geometric interpretation of Krull dimensions of -algebras
JuAe Song, Yasuhito Nakajima
We investigate Krull dimensions of semirings and semifields dealt in tropical geometry. For a congruence on a tropical Laurent polynomial semiring $\boldsymbol{T}[X_1^{\pm}, \l…
Minimal tropical basis for Bergman fan of matroid
Yasuhito Nakajima
The Bergman fan of a matroid is the intersection of tropical hyperplanes defined by the circuits. A tropical basis is a subset of the circuits set that defines the Bergman fan. Yu…