On sums of distinct representatives

Hui-Qin Cao; Zhi-Wei Sun

Acta Arithmetica (1998)

  • Volume: 87, Issue: 2, page 159-169
  • ISSN: 0065-1036

How to cite


Hui-Qin Cao, and Zhi-Wei Sun. "On sums of distinct representatives." Acta Arithmetica 87.2 (1998): 159-169. <http://eudml.org/doc/207211>.

author = {Hui-Qin Cao, Zhi-Wei Sun},
journal = {Acta Arithmetica},
keywords = {distinct representatives; Hall's theorem},
language = {eng},
number = {2},
pages = {159-169},
title = {On sums of distinct representatives},
url = {http://eudml.org/doc/207211},
volume = {87},
year = {1998},

AU - Hui-Qin Cao
AU - Zhi-Wei Sun
TI - On sums of distinct representatives
JO - Acta Arithmetica
PY - 1998
VL - 87
IS - 2
SP - 159
EP - 169
LA - eng
KW - distinct representatives; Hall's theorem
UR - http://eudml.org/doc/207211
ER -


  1. [ANR1] N. Alon, M. B. Nathanson and I. Z. Ruzsa, Adding distinct congruence classes modulo a prime, Amer. Math. Monthly 102 (1995), 250-255. Zbl0849.11081
  2. [ANR2] N. Alon, M. B. Nathanson and I. Z. Ruzsa, The polynomial method and restricted sums of congruence classes, J. Number Theory 56 (1996), 404-417. Zbl0861.11006
  3. [B] Y. Bilu, Addition of sets of integers of positive density, ibid. 64 (1997), 233-275. Zbl0877.11006
  4. [DH] J. A. Dias da Silva and Y. O. Hamidoune, Cyclic space for Grassmann derivatives and additive theory, Bull. London Math. Soc. 26 (1994), 140-146. Zbl0819.11007
  5. [EH] P. Erdős and H. Heilbronn, On the addition of residue classes mod p, Acta Arith. 9 ( 196), 4149-159. Zbl0156.04801
  6. [G] R. K. Guy, Unsolved Problems in Number Theory, 2nd ed., Springer, New York, 1994, 129-131. 
  7. [H] P. Hall, On representatives of subsets, J. London Math. Soc. 10 (1935), 26-30. Zbl0010.34503
  8. [J] N. Jacobson, Basic Algebra I, 2nd ed., W. H. Freeman and Company, New York, 1985. Zbl0557.16001
  9. [N] M. B. Nathanson, Inverse theorems for subset sums, Trans. Amer. Math. Soc. 347 (1995), 1409-1418. Zbl0835.11006

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