Dynastic order Dynastic order A dynastic order, monarchical order, or house order, is an order under royal patronage, bestowed by the head of a currently or formerly sovereign royal family as legitimate fons honorum. These are often considered part of the cultural patrimony of the royal family. They are orders of chivalry, and orders of merit just as those distributed by sovereign states, but dynastic orders were often founded or maintained to reward service to a monarch, or the monarch's subsequent dynasty. An example of this difference is seen between the Royal Victorian Order, in which appointments are made as a personal
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