Strictly monotone sequences of lower and upper bounds on Perron values and their combinatorial applications

TL;DR

This paper introduces monotone sequences of bounds on the Perron value of nonnegative matrices, demonstrating their strict monotonicity and applying them to improve bounds on rooted trees and generate log-concave and log-convex sequences.

Contribution

It develops strictly monotone sequences of bounds on Perron values and applies them to combinatorial problems involving trees and sequence properties.

Findings

Established strict monotonicity of the bounds

Improved Perron value bounds for rooted trees

Generated log-concave and log-convex sequences

Abstract

In this paper, we present monotone sequences of lower and upper bounds on the Perron value of a nonngeative matrix, and we study their strict monotonicity. Using those sequences, we provide two combinatorial applications. One is to improve bounds on Perron values of rooted trees in combinatorial settings, in order to find characteristic sets of trees. The other is to generate log-concave and log-convex sequences through the monotone sequences.