Result: Polynomial growth of sumsets in abelian semigroups
Title:
Polynomial growth of sumsets in abelian semigroups
Authors:
Source:
Journal de Théorie des Nombres de Bordeaux. 14:553-560
Publication Status:
Preprint
Publisher Information:
Cellule MathDoc/CEDRAM, 2002.
Publication Year:
2002
Subject Terms:
Document Type:
Academic journal
Article
File Description:
application/xml
ISSN:
1246-7405
DOI:
10.5802/jtnb.374
DOI:
10.48550/arxiv.math/0204052
Access URL:
http://archive.numdam.org/article/JTNB_2002__14_2_553_0.pdf
http://arxiv.org/abs/math/0204052
http://www.numdam.org/item?id=JTNB_2002__14_2_553_0
http://www.numdam.org/item/?id=JTNB_2002__14_2_553_0
https://jtnb.centre-mersenne.org/item/10.5802/jtnb.374.pdf
https://eudml.org/doc/248890
https://ui.adsabs.harvard.edu/abs/2002math......4052N/abstract
https://jtnb.centre-mersenne.org/item/?id=JTNB_2002__14_2_553_0
http://arxiv.org/abs/math/0204052
http://www.numdam.org/item?id=JTNB_2002__14_2_553_0
http://www.numdam.org/item/?id=JTNB_2002__14_2_553_0
https://jtnb.centre-mersenne.org/item/10.5802/jtnb.374.pdf
https://eudml.org/doc/248890
https://ui.adsabs.harvard.edu/abs/2002math......4052N/abstract
https://jtnb.centre-mersenne.org/item/?id=JTNB_2002__14_2_553_0
Rights:
arXiv Non-Exclusive Distribution
Accession Number:
edsair.doi.dedup.....c191c48bd2404c944bb35deacb8dc6d8
Database:
OpenAIRE
Further Information
Let S be an abelian semigroup, and A a finite subset of S. The sumset hA consists of all sums of h elements of A, with repetitions allowed. Let |hA| denote the cardinality of hA. Elementary lattice point arguments are used to prove that an arbitrary abelian semigroup has polynomial growth, that is, there exists a polynomial p(t) such that |hA| = p(h) for all sufficiently large h. Lattice point counting is also used to prove that sumsets of the form h_1A_1 + >... + h_rA_r have multivariate polynomial growth.
8 pages. LaTex. To appear in Journal de Theorie des Nombres de Bordeaux