Some Properties of the Parking Function Poset
Copyright policy )Some Properties of the Parking Function Poset
In 1980, Edelman defined a poset on objects called the noncrossing 2-partitions. They are closely related with noncrossing partitions and parking functions. To some extent, his definition is a precursor of the parking space theory, in the framework of finite reflection groups. We present some enumerative and topological properties of this poset. In particular, we get a formula counting certain chains, that encompasses formulas for Whitney numbers (of both kinds). We prove shellability of the poset, and compute its homology as a representation of the symmetric group. We moreover link it with two well-known polytopes : the associahedron and the permutohedron.
- University of Montpellier France
- UNIVERSITE DE PARIS France
- University of Marne la Vallée France
- Laboratoire d'Informatique Gaspard-Monge France
- Université de Paris France
noncrossing 2-partitions, FOS: Computer and information sciences, Discrete Mathematics (cs.DM), Exact enumeration problems, generating functions, Combinatorics of partially ordered sets, Whitney numbers, shellability, FOS: Mathematics, Mathematics - Combinatorics, parking functions, noncrossing partitions, Combinatorial aspects of partitions of integers, poset topology, representations, Elementary theory of partitions, Representations of finite symmetric groups, Representation theory of lattices, Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.), [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], symmetric group, [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], Combinatorial aspects of representation theory, Partitions of sets, Combinatorics (math.CO), Computer Science - Discrete Mathematics
noncrossing 2-partitions, FOS: Computer and information sciences, Discrete Mathematics (cs.DM), Exact enumeration problems, generating functions, Combinatorics of partially ordered sets, Whitney numbers, shellability, FOS: Mathematics, Mathematics - Combinatorics, parking functions, noncrossing partitions, Combinatorial aspects of partitions of integers, poset topology, representations, Elementary theory of partitions, Representations of finite symmetric groups, Representation theory of lattices, Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.), [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], symmetric group, [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], Combinatorial aspects of representation theory, Partitions of sets, Combinatorics (math.CO), Computer Science - Discrete Mathematics
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