Legion of Honour is headed by the Grand Chancellor, usually a retired general, and the Secretary General, a civilian administrator. The Grand Chancery also regulates the National Order of Merit and the ' (Military Medal). There are several structures funded by and operated under the authority of the Grand Chancery, like the Legion of Honour Schools (') and the Legion of Honour Museum ('). The Legion of Honour Schools are élite boarding schools in Saint-Denis and Les Loges in the forest of Saint-Germain-en-Laye. Study there is restricted to daughters, granddaughters, and great-granddaughters of members of the order, the ' or the ". There
Restricted sumset Restricted sumset In additive number theory and combinatorics, a restricted sumset has the form where formula_2 are finite nonempty subsets of a field "F" and formula_3 is a polynomial over "F". When formula_4, "S" is the usual sumset formula_5 which is denoted by "nA" if formula_6; when "S" is written as formula_8 which is denoted by formula_9 if formula_6. Note that |"S"| > 0 if and only if there exist formula_11 with formula_12. The Cauchy–Davenport theorem named after Augustin Louis Cauchy and Harold Davenport asserts that for any prime "p" and nonempty subsets "A" and "B" of the prime order