Online Encyclopedia


Online Encyclopedia
Originally appearing in Volume V06, Page 754 of the 1911 Encyclopedia Britannica.
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XP1XP2XP3... =EPX 11x x 33.. . 22 and then P is the distribution function of objects into parcels (pi 1pz2pa3•••), the distributions being such as to have the specification (sils,2°2s3a...). Multiplying out P so as to exhibit it as a sum of monomials, we get a result XP1"1XP2"2XP"3 3 ... = EEB(xt11Xt22.. . 3 el a2 a3 indicating that for distributions of specification (s°ls, 2s83...) there are 0 ways of distributing n objects denoted by (a11x22As3...) amongst n parcels denoted by (pilp22p;3...), one object in each parcel. Now observe that as before we may interchange parcel and object, and that this operation leaves the specification of the distribution unchanged. Hence the number of distributions must be the same, and if XPt"lxP"22Px"3a... =...+8(~11~22~a3...)xslx 12xe3... j ...
End of Article: XP1XP2XP3

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