Shellability of Posets of Labeled Partitions and Arrangements Defined by Root Systems
Copyright policy )Shellability of Posets of Labeled Partitions and Arrangements Defined by Root Systems
We prove that the posets of connected components of intersections of toric and elliptic arrangements defined by root systems are EL-shellable and we compute their homotopy type. Our method rests on Bibby's description of such posets by means of "labeled partitions": after giving an EL-labeling and counting homology chains for general posets of labeled partitions, we obtain the stated results by considering the appropriate subposets.
representation stability, Shellability for polytopes and polyhedra, elliptic arrangement, Shellability; Posets; Root systems; Coxeter groups; Combinatorial topology, Combinatorial aspects of simplicial complexes, Arrangements of points, flats, hyperplanes (aspects of discrete geometry), Combinatorics of partially ordered sets, Group actions on combinatorial structures, Weyl group, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), toric arrangement, hyperplane arrangement
representation stability, Shellability for polytopes and polyhedra, elliptic arrangement, Shellability; Posets; Root systems; Coxeter groups; Combinatorial topology, Combinatorial aspects of simplicial complexes, Arrangements of points, flats, hyperplanes (aspects of discrete geometry), Combinatorics of partially ordered sets, Group actions on combinatorial structures, Weyl group, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), toric arrangement, hyperplane arrangement
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