Full Resolution to Papikian's Conjecture
Combinatorics
2025-10-20 v1
Abstract
We prove Papikian's conjecture on the spectrum of the signed up-down walk on the spherical building. Namely, we show that in the spherical building of dimension n-2 and thickness q + 1, the number of distinct eigenvalues is independent of q and for q going to infinity the positive eigenvalues converge to n-1, ... , n-i.
Cite
@article{arxiv.2510.15161,
title = {Full Resolution to Papikian's Conjecture},
author = {Paul Vollrath},
journal= {arXiv preprint arXiv:2510.15161},
year = {2025}
}