TY - JOUR
T1 - The Dicks-Ivanov problem and the Hamidoune problem
AU - Dicks, Warren
AU - Serra, Oriol
PY - 2013/11/1
Y1 - 2013/11/1
N2 - We report on what we call the Hamidoune problem, inspired by a problem by Dicks and Ivanov. The problem asks if the inequality |A|+|B|-12|AB|-12|A{dot operator}2B|≤max{2,|gH|:H≤G,g∈G,gH⊆A{dot operator}2B} holds when A and B are finite subsets of a group G, each one with at least two elements, and A{dot operator}2B denotes the set of elements which can be written in at least two different ways as a product of one element in A and one in B. © 2013 Elsevier Ltd.
AB - We report on what we call the Hamidoune problem, inspired by a problem by Dicks and Ivanov. The problem asks if the inequality |A|+|B|-12|AB|-12|A{dot operator}2B|≤max{2,|gH|:H≤G,g∈G,gH⊆A{dot operator}2B} holds when A and B are finite subsets of a group G, each one with at least two elements, and A{dot operator}2B denotes the set of elements which can be written in at least two different ways as a product of one element in A and one in B. © 2013 Elsevier Ltd.
UR - https://www.scopus.com/pages/publications/84881027739
U2 - 10.1016/j.ejc.2013.05.015
DO - 10.1016/j.ejc.2013.05.015
M3 - Article
SN - 0195-6698
VL - 34
SP - 1326
EP - 1330
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
IS - 8
ER -