Combinatorial complexity of convex sequences

A Iosevich, S Konyagin, M Rudnev, VV Ten

Research output: Contribution to journalArticle (Academic Journal)peer-review

20 Citations (Scopus)


We show that the equation s(i1) +s(i2) +... +s(id) =si(d+1) + - +si(2d) has O (N2d-2+2-d+1) solutions for any strictly convex sequence {s(i)}(i=1)(N) without any additional arithmetic assumptions. The proof is based on weighted incidence theory and an inductive procedure which allows us to deal with higher-dimensional interactions effectively. The terminology "combinatorial complexity" is borrowed from [CES+] where much of our higher-dimensional incidence theoretic motivation comes from.
Translated title of the contributionCombinatorial complexity of convex sequences
Original languageEnglish
Pages (from-to)143 - 158
Number of pages16
JournalDiscrete and Computational Geometry
Volume35 (1)
Publication statusPublished - Jan 2006

Bibliographical note

Publisher: Springer
Other identifier: IDS Number: 988KX


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