Linear independences of maps associated to partitions
Combinatorics
2019-06-26 v1
Abstract
Given a suitable collection of partitions of sets, there exists a connection to easy quantum groups via intertwiner maps. A sufficient condition for this correspondence to be one-to-one are particular linear independences on the level of those maps. In the case of non-crossing partitions, a proof of this linear independence can be traced back to a matrix determinant formula, developed by W. Tutte. We present a revised and adapted version of Tutte's work and the link to the problem above, believing that this self-contained article will assist others in the field of easy quantum groups. In particular, we fixed some errors in the original work and adapted notations, definitions, statements and proofs.
Keywords
Cite
@article{arxiv.1906.10533,
title = {Linear independences of maps associated to partitions},
author = {Stefan Jung},
journal= {arXiv preprint arXiv:1906.10533},
year = {2019}
}