On the Spectrum of Finite, Rooted Homogeneous Trees

Daniel N. Rockmore; Daryl R. DeFord

On the Spectrum of Finite, Rooted Homogeneous Trees

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1903.07134 v2 pith:VFFF35KP submitted 2019-03-17 math.RT cs.OHmath.CO

Daryl R. DeFord , Daniel N. Rockmore This is my paper · ORCID

classification math.RTcs.OHmath.CO

keywords branchingeigenvaluesfiniterootedspectrumtreesadjacencycase

verification ladder T0 review T1 audit T2 compute T3 formal

0 comments

read the original abstract

In this paper we study the adjacency spectrum of families of finite rooted trees with regular branching properties. In particular, we show that in the case of constant branching, the eigenvalues are realized as the roots of a family of generalized Fibonacci polynomials and produce a limiting distribution for the eigenvalues as the tree depth goes to infinity. We indicate how these results can be extended to periodic branching patterns and also provide a generalization to higher order simplicial complexes.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Topological states and flat bands in exactly solvable decorated Cayley trees
cond-mat.mes-hall 2025-11 conditional novelty 7.0 of 10

Flat bands on decorated Cayley trees map exactly onto topological edge states of 1D SSH chains, and persist on infinite Bethe lattices by a covering construction.

Pith tools