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arXiv · 1403.6053

On the Basis of the Burnside Ring of a Fusion System

Matthew Gelvin·Sune Precht Reeh·Ergun Yalcin
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Abstract

We consider the Burnside ring $A(\mathcal{F})$ of $\mathcal{F}$-stable $S$-sets for a saturated fusion system $\mathcal{F}$ defined on a $p$-group $S$. It is shown by S. P. Reeh that the monoid of $\mathcal{F}$-stable sets is a free commutative monoid with canonical basis $\{α_P\}$. We give an explicit formula that describes $α_P$ as an $S$-set. In the formula we use a combinatorial concept called broken chains which we introduce to understand inverses of modified Möbius functions.

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Matthew Gelvin, Sune Precht Reeh, Ergun Yalcin. 2014-03-28. On the Basis of the Burnside Ring of a Fusion System. https://arxiv.org/abs/1403.6053

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