Infinite families of triangle presentations

Alex Loué
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Abstract

A triangle presentation is a combinatorial datum that encodes the action of a group on a $2$-dimensional triangle complex with prescribed links, which is simply transitive on the vertices. We provide the first infinite family of triangle presentations that give rise to lattices in exotic buildings of type $\widetilde{\text{A}_2}$ of arbitrarily large order. Our method also gives rise to infinite families of triangle presentations for other link types, such as opposition complexes in Desarguesian projective planes.
三角形无穷族
三角形呈现是一种组合数据,它编码了一个组对一个具有规定链接的 2 美元维三角形复数的作用,这种作用在顶点上是简单传递的。我们提供了第一个无穷三角呈现族,它能在任意大阶的奇异建筑中产生格点类型(type$\widetilde{\text{A}_2}$)。我们的方法还为其他链接类型,例如德萨古投影面中的位置复数,提供了无穷三角呈现族。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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