2023/12/22 by Krystian Gajdzica, Gajdzica, Krystian, Piotr Miska +3
Mathematics · #11P84 #Analytic Number Theory Research #Analytic and geometric function theory #Combinatorics (math.CO) #FOS: Mathematics #Functional Equations Stability Results #Number Theory (math.NT) #Primary 11P82 #Secondary 05A17
paper · pdf · doi:10.48550/arxiv.2312.14501
openalex publication_date 2023/12/22 · openalex created_date 2023/12/26 · openalex updated_date 2026/07/28
In recent literature concerning integer partitions one can find many results related to both the Bessenrodt-Ono type inequalities and log-concavity property. In this note we offer some general approach to this type of problems. More precisely, we prove that under some mild conditions on an increasing function F of at most exponential growth satisfying the condition F(ℕ)⊂ ℝ+, we have F(a)F(b)>F(a+b) for sufficiently large positive integers a, b. Moreover, we show that if the sequence (F(n))_n≥ n0 is log-concave and \limsupn→ +∞F(n+n0)/F(n)