2017/07/20 by Michael Dougherty, Jon McCammond, Dougherty, Michael +1
Mathematics · Computer Science · #Advanced Combinatorial Mathematics #Topological and Geometric Data Analysis #Advanced Algebra and Logic
paper · pdf · doi:10.48550/arxiv.1707.06620
There are two natural simplicial complexes associated to the noncrossing\npartition lattice: the order complex of the full lattice and the order complex\nof the lattice with its bounding elements removed. The latter is a complex that\nwe call the noncrossing partition link because it is the link of an edge in the\nformer. The first author and his coauthors conjectured that various collections\nof simplices of the noncrossing partition link (determined by the undesired\nparking spaces in the corresponding parking functions) form contractible\nsubcomplexes. In this article we prove their conjecture by combining the fact\nthat the star of a simplex in a flag complex is contractible with the second\nauthor's theory of noncrossing hypertrees.\n