Abstract: A logistic was derived by Mr H.C. Rajpoot in March, 2010 which was formulated in a generalised form by him in Feb, 2014 by using some arbitrary terms to deal with complex problems of linear permutations. It is used to find out the correct order (called rank) of any randomly selected (or a given) linear permutation (like words, numbers & all other linear permutations) from a set of all the linear permutations arranged in a correct order (sequence). It is an expansion (series) formula of which each term corresponds to a certain article of any linear permutation. It is also applicable to position the linear permutations in correct order provided that the articles have at least one easily distinguishable property like appearance in shape, size, colour, surface-design etc. & all are equally significant at all the places (positions) in all possible linear arrangements. For ease of understanding, for a given alphabetic word or a positive integral number with ‘n’ letters or non-zero digits respectively. It has three new arbitrary parameters as which are expanded in a finite series. The values of these parameters depend on former (leading) articles, permutations of successive articles &repeatability of article, &The number of terms in that series is equal to total no. of articles (like letters, digits etc.) in any linear permutation (like word, number etc.).
Keywords: Linear permutation,
Title: HCR’s Rank or Series Formula
Author: Harish Chandra Rajpoot
International Journal of Mathematics and Physical Sciences Research
ISSN 2348-5736 (Online)
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