272 citations · 1k across the 53 of their papers we have counts for
53 papers
Relation between generalized and ordinary cluster algebras
Ryota Akagi, Tomoki Nakanishi
Recently, Ramos and Whiting showed that any generalized cluster algebra of geometric type is isomorphic to a quotient of a subalgebra of a certain cluster algebra. Based on their i…
reduction of 4D Schur index and 3D mass-deformed partition function
Tomoki Nakanishi, Takahiro Nishinaka
We study the compactification of 4D SYM on from the viewpoint of the superconformal index. In the cases that the gauge group of the 4D SYM is and $Usp(…
Local and global patterns of rank 3 -fans of totally-infinite type
Tomoki Nakanishi
We focus on the -fans associated with cluster patterns whose initial exchange matrices are of infinite type. We study the asymptotic behavior of the -vectors around the initi…
Cluster Algebras and Dilogarithm Identities
Tomoki Nakanishi
This is a reasonably self-contained exposition of the fascinating interplay between cluster algebras and the dilogarithm in the past two decades. The dilogarithm has a long and ric…
Addendum to "Structure of seeds in generalized cluster algebras"
Tomoki Nakanishi
This is Addendum to ``Structure of seeds in generalized cluster algebras'', Pacific J. Math. {277} (2015), 201--218. We extend the class of generalized cluster algebras studied the…
Liouville Irregular States of Half-Integer Ranks
Ryo Hamachika, Tomoki Nakanishi, Takahiro Nishinaka +1
We conjecture a set of differential equations that characterizes the Liouville irregular states of half-integer ranks, which extends the generalized AGT correspondence to all the $…