Alternating paths of fully packed loops and inversion number
Combinatorics
2013-01-08 v3
Abstract
We consider the set of alternating paths on a fixed fully packed loop of size n. This set is in bijection with the set of fully packed loops of size n. Furthermore, for a special choice of fully packed loop, we demonstrate that the set of alternating paths are nested osculating loops, which we call Dyck islands. Dyck islands can be constructed as a union of lattice Dyck paths, and we use this structure to give a simple graphical formula for the calculation of the inversion number of an alternating sign matrix.
Keywords
Cite
@article{arxiv.1202.2483,
title = {Alternating paths of fully packed loops and inversion number},
author = {Stephen Ng},
journal= {arXiv preprint arXiv:1202.2483},
year = {2013}
}