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On the modular sumset partition problem

Author
Llado, A.; Moragas, J.
Type of activity
Journal article
Journal
European journal of combinatorics
Date of publication
2012-04-28
Volume
33
Number
4
First page
427
Last page
434
DOI
https://doi.org/10.1016/j.ejc.2011.09.001 Open in new window
Project funding
2009SGR01387
URL
http://cataleg.upc.edu/record=b1206976~S1*cat Open in new window
Abstract
A sequence m 1=m 2=¿;=m k of k positive integers isn-realizable if there is a partition X 1, X 2,..., X k of the integer interval [1, n] such that the sum of the elements in X i is m i for each i=1, 2,..., k. We consider the modular version of the problem and, by using the polynomial method by Alon (1999) [2], we prove that all sequences in Z/pZ of length k=(p-1)/2 are realizable for any prime p=3. The bound on k is best possible. An extension of this result is applied to give two results of p-...
Group of research
GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics

Participants