Conjectured factorization and recursive construction for Laplacian characteristic polynomials in DSC(1)
Establish that for all n the Laplacian characteristic polynomial factorizes as Π_n(λ) = −λ \prod_{i=1}^n π_i(λ) with π_i(λ) generated recursively by Eqs. (585) and (pi-rec), i.e., that the identified recurrence pattern holds at all generations.
References
We then identify a recurrence relation and conjecture that this pattern continues for larger $n$.
— Deterministic simplicial complexes
(Dorogovtsev et al., 10 Jul 2025) in Section 3.5 (Laplacian spectrum of the DSC(1) model); after Eq. (Pi-factor) introducing the recursive construction