KUN-MAO CHAOChu, A.-C.A.-C.ChuJansson, J.J.JanssonLemence, R.S.R.S.LemenceMancheron, A.A.Mancheron2020-04-162020-04-16201203029743https://www.scopus.com/inward/record.uri?eid=2-s2.0-84861005661&doi=10.1007%2f978-3-642-29952-0_21&partnerID=40&md5=3371f88421d0420265319785dc25201dWe study the asymptotic behavior of a new type of maximization recurrence, defined as follows. Let k be a positive integer and p k(x) a polynomial of degree k satisfying p k(0) = 0. Define A 0 = 0 and for n ≥ 1, let A n = max 0≤i<n{A i+n kp k(i/n)}. We prove that lim n→∞A n/n n = sup{pk(x)/1-x k : 0≤x<1}. We also consider two closely related maximization recurrences S n and S′ n, defined as S 0 = S′ 0 = 0, and for n ≥ 1, S n = max 0≤i<n{S i + i(n-i)(n-i-1)/2} and S′ n = max 0≤i<n{S′ i + ( 3 n-i) + 2i( 2 n-i) + (n-i)( 2 i)}. We prove that lim n→∞ S′n/3( 3 n) = 2(√3-1)/3 ≈ 0.488033..., resolving an open problem from Bioinformatics about rooted triplets consistency in phylogenetic networks. © 2012 Springer-Verlag.Asymptotic behaviors; Asymptotic limits; Phylogenetic Networks; Positive integers; Rooted triplets; Asymptotic analysis; Bioinformaticsconference paper10.1007/978-3-642-29952-0_212-s2.0-84861005661