2021
DOI: 10.48550/arxiv.2105.11278
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On the Number of Arrows of Cluster Quivers

Abstract: Let Q (resp. Q) be an extended exchange (resp. exchange) cluster quiver of finite mutation type. We introduce the distribution set of the number of arrows for M ut[ Q] (resp. M ut[Q]), give the maximum and minimum numbers of the distribution set and establish the existence of an extended complete walk (resp. a complete walk). As a consequence, we prove that the distribution set for M ut [ Q] (resp. M ut[Q]) is continuous except the exceptional cases.In case of cluster quivers Q inf of infinite mutation type… Show more

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