Quiver mutation sequences and q-binomial identities

Akishi Kato; Yuma Mizuno; Yuji Terashima

doi:10.1093/imrn/rnx108

Quiver mutation sequences and q-binomial identities

Akishi Kato, Yuma Mizuno, Yuji Terashima

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this article, first we introduce a quantity called a partition function for a quiver mutation sequence. The partition function is a generating function whose weight is a q-binomial associated with each mutation. Then, we show that the partition function can be expressed as a ratio of products of quantum dilogarithms. This provides a systematic way of constructing various q-binomial multisum identities.

Original language	English
Pages (from-to)	7335-7358
Number of pages	24
Journal	International Mathematics Research Notices
Volume	2018
Issue number	23
DOIs	https://doi.org/10.1093/imrn/rnx108
Publication status	Published - 2018 Dec 4

ASJC Scopus subject areas

Mathematics(all)

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10.1093/imrn/rnx108

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title = "Quiver mutation sequences and q-binomial identities",

abstract = "In this article, first we introduce a quantity called a partition function for a quiver mutation sequence. The partition function is a generating function whose weight is a q-binomial associated with each mutation. Then, we show that the partition function can be expressed as a ratio of products of quantum dilogarithms. This provides a systematic way of constructing various q-binomial multisum identities.",

author = "Akishi Kato and Yuma Mizuno and Yuji Terashima",

note = "Funding Information: This work is partially supported by the Japan Society for the Promotion of Science (JSPS) Grants-in-Aid for Scientific Research (KAKENHI) [JP16K13752, JP16H03931, 25400083], and by Japan Science and Technology Agency (JST) Core Research for Evolutionary Science and Technology (CREST) [JPMJCR14D6].",

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AU - Kato, Akishi

AU - Mizuno, Yuma

AU - Terashima, Yuji

N1 - Funding Information: This work is partially supported by the Japan Society for the Promotion of Science (JSPS) Grants-in-Aid for Scientific Research (KAKENHI) [JP16K13752, JP16H03931, 25400083], and by Japan Science and Technology Agency (JST) Core Research for Evolutionary Science and Technology (CREST) [JPMJCR14D6].

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Y1 - 2018/12/4

N2 - In this article, first we introduce a quantity called a partition function for a quiver mutation sequence. The partition function is a generating function whose weight is a q-binomial associated with each mutation. Then, we show that the partition function can be expressed as a ratio of products of quantum dilogarithms. This provides a systematic way of constructing various q-binomial multisum identities.

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