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On PM-mapping class monoids
Toshinori Miyatani
In this paper, we introduce PM-mapping class monoids. Braid groups and mapping class groups have many features in common. Similarly to the notion of braid PM-monoid, PM-mapping cla…
On knot semigroups and Gelfand-Kirillov dimensions
Toshinori Miyatani
A knot semigroup is defined by A. Vernitski. A. Vernitski conjectured that the knot semigroup of the 2-bridge knot is isomorphic to an alternating sum semigroup. To support this co…
On PM-monoids and braid PM-monoids
Toshinori Miyatani
In this paper, we shall introduce two monoids. One is called a PM-monoid which contains the symmetric group, the other is called a braid PM-monoid which contains the braid group. W…
Euler characteristic reciprocity for chromatic, flow and order polynomials
Takahiro Hasebe, Toshinori Miyatani, Masahiko Yoshinaga
The Euler characteristic of a semialgebraic set can be considered as a generalization of the cardinality of a finite set. An advantage of semialgebraic sets is that we can define "…