Control of cancellations that restrain the growth of a binomial recursion

Summary, in English

We study a recursion that generates real sequences depending on a parameter x. Given a negative x the growth of the sequence is very difficult to estimate due to canceling terms. We reduce the study of the recursion to a problem about a family of integral operators, and prove that for every parameter value except -1, the growth of the sequence is factorial. In the combinatorial part of the proof we show that when x=-1 the resulting recurrence yields the sequence of alternating Catalan numbers, and thus has exponential growth. We expect our methods to be useful in a variety of similar situations.

• Författare: Magnus Aspenberg; Rodrigo Perez
• Avdelning/ar: Matematik LTH; Dynamical systems
• Publiceringsår: 2015
• Språk: Engelska
• Sidor: 1666-1700
• Publikation/Tidskrift/Serie: Journal of Geometric Analysis
• Volym: 25
• Issue: 3
• Länkar: http://dx.doi.org/10.1007/s12220-014-9489-y
• Dokumenttyp: Artikel i tidskrift
• Förlag: Springer
• Ämne: Mathematics
• Nyckelord: Catalan numbers; Factorial growth; Integral operators
• Status: Published
• Forskningsgrupp: Dynamical systems
• ISBN/ISSN/Övrigt: ISSN: 1559-002X