2 research outputs found
Some natural extensions of the parking space
We construct a family of modules indexed by with
the property that upon restriction to they recover the classical
parking function representation of Haiman. The construction of these modules
relies on an -action on a set that is closely related to the set of
parking functions. We compute the characters of these modules and use the
resulting description to classify them up to isomorphism. In particular, we
show that the number of isomorphism classes is equal to the number of divisors
of satisfying . In the cases and
, we compute the number of orbits. Based on empirical evidence, we
conjecture that when , our representation is -positive and is in fact
the (ungraded) extension of the parking function representation constructed by
Berget and Rhoades.Comment: 16 pages; comments welcom
Poset Topology: Tools and Applications
These lecture notes for the IAS/Park City Graduate Summer School in Geometric
Combinatorics (July 2004) provide an overview of poset topology. These notes
include introductory material, as well as recent developments and open
problems. Some of the topics covered are: subspace arrangements, graph
complexes, group actions on poset homology, shellability, recursive techniques,
and fiber theorems.Comment: 119 pages, to appear in the volume "Geometric Combinatorics" of the
IAS/Park City Mathematics serie