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arXiv · 1606.00958

The formula for the permutation of mutation sequences in $A_n$ straight orientation

Kiyoshi Igusa·Ying Zhou
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Abstract

In this paper we state and prove a formula for the permutations associated to reddening and loop sequences in $A_n$ straight orientation using the picture group. In particular this applies to maximal green sequences in $A_n$ straight orientation. Furthermore we extend the definition and formula of the associated permutation to arbitrary mutation sequences based on our results. We introduce the concept of standard matrices which gives a canonical order on indecomposable components of cluster-tilting objects. Preservation of standardness of C-matrices by a combination of a mutation and its associated permutation gives the formula.

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Kiyoshi Igusa, Ying Zhou. 2016-06-03. The formula for the permutation of mutation sequences in $A_n$ straight orientation. https://arxiv.org/abs/1606.00958

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