272 citations · 1k across the 53 of their papers we have counts for
9 papers · 1 filter
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…
Synchronicity phenomenon in cluster patterns
Tomoki Nakanishi
It has been known that several objects such as cluster variables, coefficients, seeds, and -seeds in different cluster patterns with common exchange matrices share the same peri…
Hamiltonian and Lagrangian formalisms of mutations in cluster algebras and application to dilogarithm identities
Michael Gekhtman, Tomoki Nakanishi, Dylan Rupel
We introduce and study a Hamiltonian formalism of mutations in cluster algebras using canonical variables, where the Hamiltonian is given by the Euler dilogarithm. The correspondin…
Companion cluster algebras to a generalized cluster algebra
Tomoki Nakanishi, Dylan Rupel
We study the -vectors, -vectors, and -polynomials for generalized cluster algebras satisfying a normalization condition and a power condition recovering classical recursio…
Quantum generalized cluster algebras and quantum dilogarithms of higher degrees
Tomoki Nakanishi
We extend the notion of the quantization of the coefficients of the ordinary cluster algebras to the generalized cluster algebras by Chekhov and Shapiro. In parallel to the ordinar…