major index

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1: 26.16 Multiset Permutations

… ►The definitions of inversion number and major index can be extended to permutations of a multiset such as

351322453154\in\mathfrak{S}_{\{1^{2},2^{2},3^{3},4^{2},5^{3}\}}

. …

2: 26.14 Permutations: Order Notation

… ►The major index is the sum of all positions that mark the first element of a descent: ►

26.14.2

\mathop{\mathrm{maj}}(\sigma)=\sum_{\begin{subarray}{c}1\leq j<n\\ \sigma(j)>\sigma(j+1)\end{subarray}}j.

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Symbols:: $j$ : nonnegative integer, $n$ : nonnegative integer, $\sigma$ : permutation and $\mathop{\mathrm{maj}}(\sigma)$ : major index
Permalink:: http://dlmf.nist.gov/26.14.E2
Encodings:: pMML, png, TeX
See also:: Annotations for §26.14(i), §26.14 and Ch.26

… ►The major index is also called the greater index of the permutation. …

3: Preface

… ►Olver was responsible for organizing and editing the mathematical content after receiving it from the authors; for communicating with the associate editors, authors, validators, and other technical experts; and for assembling the Notations section and the Index. …Boisvert and Clark were responsible for advising and assisting in matters related to the use of information technology and applications of special functions in the physical sciences (and elsewhere); they also participated in the resolution of major administrative problems when they arose. … ►

Abdou Youssef, Mathematics and Search Indexing, George Washington University and NIST

… ►Youssef was responsible for mathematics search indexing and query processing. …

4: 18.39 Applications in the Physical Sciences

… ►Bound state solutions to the relativistic Dirac Equation, for this same problem of a single electron attracted by a nucleus with

Z

protons, involve Laguerre polynomials of fractional index. … ►A major difficulty in such calculations, loss of precision, is addressed in Gautschi (2009) where use of variable precision arithmetic is discussed and employed. …