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Encyclopedia Britannica



XP1XP2XP3

This article appears in Volume V06, Page 754 of the Encyclopedia Britannica.

Encyclopedia Britannica - Main :: WIL-YAK
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,22s3a...). 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
  (sls, 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 ...


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