TY - MGZN
AU - Llado, A.
AU - Moragas, J.
T2 - European journal of combinatorics
Y1 - 2012
VL - 33
IS - 4
SP - 427
EP - 434
DO - 10.1016/j.ejc.2011.09.001
UR - http://cataleg.upc.edu/record=b1206976~S1*cat
AB - 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-realizable sequences in the integers. The first one is an extension, for n a prime, of the best known sufficient condition for n-realizability. The second one shows that, for n=(4k) 3, an n-feasible sequence of length k isn-realizable if and only if it does not contain forbidden subsequences of elements smaller than n, a natural obstruction forn-realizability. © 2011 Elsevier Ltd.
TI - On the modular sumset partition problem
ER -