2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56526We present a few combinatorial identities which were encountered in our work on the spectral theory of quantum graphs. They establish a new connection between the theory of random matrix ensembles and combinatorics.16 pages, RevTeX, 1 figureMathematical PhysicsCombinatoricstext