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

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