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math.CO2026
Log-Concavity and Infinite Log-Concavity of Linear Recurrent Sequences with Linear Coefficients via Companion Matrix Methods
Piero Giacomelli
We study log-concavity properties of real sequences satisfying a -th order linear recurrence whose coefficients are linear functions of ; the so-called P-re…
math.CO2026
The Bollobás--Nikiforov Conjecture for Complete Multipartite Graphs and Dense -Free Graphs
Piero Giacomelli
The Bollobás--Nikiforov conjecture asserts that for any graph with edges and clique number , \[ λ_1^2(G) + λ_2^2(G) \;\leq\; 2\!\left(1 - \frac{1}{ω(G)}\righ…
math.CO2025
On Log-Concave Operator Acting on Sequences and Series
Piero Giacomelli
In this paper, we investigate the properties of sequences and series under the action of the log-concave operator \(\mathcal{L}\). We explore the relationship between the convergen…