13,293 research outputs found
On the Smarandache totient function and the Smarandache power sequence
Talking about Smarandache power function, Smarandache totient function, convergence
On Structure of cluster algebras of geometric type I: In view of sub-seeds and seed homomorphisms
Our motivation is to build a systematic method in order to investigate the
structure of cluster algebras of geometric type.
The method is given through the notion of mixing-type sub-seeds, the theory
of seed homomorphisms and the view-point of gluing of seeds. As an application,
for (rooted) cluster algebras, we completely classify rooted cluster
subalgebras and characterize rooted cluster quotient algebras in detail. Also,
we build the relationship between the categorification of a rooted cluster
algebra and that of its rooted cluster subalgebras.
Note that cluster algebras of geometric type studied here are of the
sign-skew-symmetric case.Comment: 41 page
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