Control of cancellations that restrain the growth of a binomial recursion
(2015) In Journal of Geometric Analysis 25(3). p.1666-1700- Abstract
- 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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/4251395
- author
- Aspenberg, Magnus LU and Perez, Rodrigo
- organization
- publishing date
- 2015
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Catalan numbers, Factorial growth, Integral operators
- in
- Journal of Geometric Analysis
- volume
- 25
- issue
- 3
- pages
- 1666 - 1700
- publisher
- Springer
- external identifiers
-
- wos:000356515800014
- scopus:84931560812
- ISSN
- 1559-002X
- DOI
- 10.1007/s12220-014-9489-y
- language
- English
- LU publication?
- yes
- id
- 005c5b1c-2e31-4e43-ac43-24dec369d7c9 (old id 4251395)
- date added to LUP
- 2016-04-01 09:56:18
- date last changed
- 2022-04-27 17:00:58
@article{005c5b1c-2e31-4e43-ac43-24dec369d7c9,
abstract = {{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.}},
author = {{Aspenberg, Magnus and Perez, Rodrigo}},
issn = {{1559-002X}},
keywords = {{Catalan numbers; Factorial growth; Integral operators}},
language = {{eng}},
number = {{3}},
pages = {{1666--1700}},
publisher = {{Springer}},
series = {{Journal of Geometric Analysis}},
title = {{Control of cancellations that restrain the growth of a binomial recursion}},
url = {{http://dx.doi.org/10.1007/s12220-014-9489-y}},
doi = {{10.1007/s12220-014-9489-y}},
volume = {{25}},
year = {{2015}},
}