Actions and Identities on Set Partitions
Name
Marberg-2012-Actions and identities.pdf
Size
420.01 KB
Format
Adobe PDF
Checksum (MD5)
8915efdc354bd7ae8c977b0a878b3f7a
Author(s)
Marberg, Eric
Date Issued
January 2012
Journal
Electronic Journal of Combinatorics
Publisher
Electronic Journal of Combinatorics
Citation
Marberg, Eric. "Actions and Identities on Set Partitions." Electronic Journal of Combinatorics, Volume 19, Issue 1 (2012).
Version
Final published version
Abstract
A labeled set partition is a partition of a set of integers whose arcs are labeled by nonzero elements of an abelian group A. Inspired by the action of the linear characters of the unitriangular group on its supercharacters, we define a group action of A[superscript n] on the set of A-labeled partitions of an (n+1)-set. By investigating the orbit decomposition of various families of set partitions under this action, we derive new combinatorial proofs of Coker's identity for the Narayana polynomial and its type B analogue, and establish a number of other related identities. In return, we also prove some enumerative results concerning André and Neto's supercharacter theories of type B and D.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.37236/1992
