Abstract
& Keywords
A set formula named as HCR’s
Rank Formula or HCR’s Series Formula has been derived by inverse relation. It is an expansion formula based on logistics of which each term
corresponds to a certain letter of an
alphabetic word or a certain non-zero
digit of a positive integral number.
If a given word/positive integral number has total 
no. of the letters/non-zero digits then the correct
alphabetic/numeric order (say rank (R)), of any of the words/numbers obtained
by permuting all the letters/digits, is given as follows
no. of the letters/non-zero digits then the correct
alphabetic/numeric order (say rank (R)), of any of the words/numbers obtained
by permuting all the letters/digits, is given as follows
It is equally applicable for finding out alphabetic-order (called rank)
of a word or numeric-order (increasing or decreasing) of a positive
integral number having non-zero digits. Although it does not have any
Mathematical Origin but it gives correct results to deal with the complex
problems of permutation in Algebra. This formula equally deals
with the permutations of words having repetitive
& non repetitive letters and positive
integral numbers, having repetitive & non repetitive, non-zero digits.
It has three new arbitrary terms as 
which are formulated in a finite series (expansion). The number of terms in the series is
equal to the no. of total letters in a given word or total non-zero digits in a
given positive integral number.
which are formulated in a finite series (expansion). The number of terms in the series is
equal to the no. of total letters in a given word or total non-zero digits in a
given positive integral number. 
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