Alternating paths of fully packed loops and inversion number

Details Alternating paths of fully packed loops and inversion number Alternating paths of fully packed loops and inversion number

2012-02-12

arxiv.org/abs/1202.2483v1

Mathematics

Combinatorics

Scientific paper

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. This set is also shown to be a self-dual distributive lattice. In the hope of shedding light on a bijective proof of the alternating sign matrix-descending plane partition (ex-)conjecture, we provide a simple characterization of the inversion number in terms of loops of Dyck islands.

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