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arXiv · 2507.06182

From i-boxes to signed words

Alessandro Contu·Fan Qin·Qiaoling Wei
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Abstract

The combinatorics of i-boxes has recently been introduced by Kashiwara--Kim--Oh--Park in the study of cluster algebras arising from the representation theory of quantum affine algebras. In this article, we associate to each chain of i-boxes a signed word, which canonically determines a cluster seed following Berenstein--Fomin--Zelevinsky. By bridging these two different languages, we are able to provide a quick solution to the problem of explicit determining the exchange matrices associated with chains of i-boxes.

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BibTeXRIS

Alessandro Contu, Fan Qin, Qiaoling Wei. 2025-07-08. From i-boxes to signed words. https://doi.org/10.2140/pjm.2026.342.63

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