Year: 2007
Type: preprint
Abstract: Partitions of [n]={1,2,...,n} into sets of lists are counted by sequence number A000262 in the On-Line Encyclopedia of Integer Sequences. They are somewhat less numerous than partitions of [n] into lists of sets, A000670. Here we observe that the former are actually equinumerous with partitions of [n] into lists of *noncrossing* sets and give a bijective proof. We show that partitions of [n] into sets of noncrossing lists are counted by A088368 and generalize this result to introduce a transform on integer sequences that we dub the "noncrossing partition" transform. We also derive recurrence relations to count partitions of [n] into lists of noncrossing lists.
Source: arXiv (Cornell University)
Author: Callan, David
Institution: University of Wisconsin–Madison
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1610334292