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arXiv · 2402.05656

Characterisation of band bricks over certain string algebras and a variant of perfectly clustering words

Annoy Sengupta·Amit Kuber
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Abstract

Generalising a recent work of Dequ\^ene et al. on the connection between perfectly clustering words and band bricks over a particular family of gentle algebras, we characterise band bricks over string algebras whose underlying quiver is acyclic in terms of weakly perfectly clustering pairs of words -- a variant of perfectly clustering words. As a consequence, we characterise band semibricks over all such algebras. Furthermore, the combination of our result and a result of Mousavand and Paquette provides an algorithm to determine whether such a string algebra is brick-infinite.

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Annoy Sengupta, Amit Kuber. 2024-02-08. Characterisation of band bricks over certain string algebras and a variant of perfectly clustering words. https://arxiv.org/abs/2402.05656

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