Shellings are ubiquitous tools in the study of simplicial complexes, and the existence of a shelling implies strong topological, algebraic, and combinatorial properties for a complex. In this talk, we consider shellings induced by the order of the vertices of a complex. A classic theorem of Björner in this vein states that a pure simplicial complex is a matroid independence complex if and only if every order on its vertices induces a shelling. We consider complexes defined via various vertex order conditions and determine which of these vertex orders induce shellings. Joint with Marta Pavelka.
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