The CLLC conjecture holds for cyclic outer permutations
Combinatorics
2015-11-11 v1
Abstract
Recently, Gross et al. posed the LLC conjecture for the locally log-concavity of the genus distribution of every graph, and provided an equivalent combinatorial version, the CLLC conjecture, on the log-concavity of the generating function counting cycles of some permutation compositions. In this paper, we confirm the CLLC conjecture for cyclic permutations, with the aid of Hultman numbers and by applying the Hermite--Biehler theorem on the generating function of Stirling numbers of the first kind. This leads to a further conjecture that every local genus polynomial is real-rooted.
Cite
@article{arxiv.1511.03139,
title = {The CLLC conjecture holds for cyclic outer permutations},
author = {Jonathan L. Gross and Toufik Mansour and Thomas W. Tucker and David G. L. Wang},
journal= {arXiv preprint arXiv:1511.03139},
year = {2015}
}
Comments
12 pages