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Abstract: Let \Delta be a finite building or, more generally, a thick spherical andlocally finite building. The chamber graph G\Delta, whose edges are thepairs of adjacent chambers in \Delta, is known to be q-regular for a certainnumber q=q\Delta. Our main result is that G\Delta is q-connected in thesense of graph theory.Similar results are proved for the chamber graphs of Coxeter complexes andfor order complexes of geometric lattices.



Author: Anders Björner, Kathrin Vorwerk

Source: https://arxiv.org/



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