Accession Number : AD0718148

Title :   Entropies of Partitions,

Corporate Author : ILLINOIS UNIV URBANA BIOLOGICAL COMPUTER LAB

Personal Author(s) : Tuttle,H. ; Ashby,W. R. ; Kokjer,K.

Report Date : 30 SEP 1970

Pagination or Media Count : 136

Abstract : Let (f sub i) be the frequency of occurrence of events in a universe with n distinguishable event categories, i=1,2,3,...,n, with Summation from 1 to n of (f sub i)=N. The entropy of this universe is then defined by H = minus summation from 1 to n of ((p sub i) log to the base 2 of (p sub i)) bits where the (p sub i)'s are the relative frequencies (P sub i) = (f sub i)/N. On the other hand, the collection of (f sub i)'s represents a particular partition of N into precisely n parts. Since in the majority of observations it is the (f sub i)'s that are directly measured, this Table gives the entropy for partitions (f sub i) for N up to 24 directly, supplies major help for calculating the entropy of partitions for N up to 48, and is useful for cases in which N is less or about 200. (Author)

Descriptors :   (*COMBINATORIAL ANALYSIS, TABLES(DATA)), (*INFORMATION THEORY, COMBINATORIAL ANALYSIS), NUMERICAL ANALYSIS, COMPILERS

Subject Categories : Numerical Mathematics
      Cybernetics

Distribution Statement : APPROVED FOR PUBLIC RELEASE