Lehmer code: Difference between revisions

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{{Short description|Scheme for numbering permutations}}

In [[mathematics]] and in particular in [[combinatorics]], the '''Lehmer code''' is a particular way to [[encoding|encode]] each possible [[permutation]] of a sequence of ''n'' numbers. It is an instance of a scheme for [[Permutation#Numbering permutations|numbering permutations]] and is an example of an [[inversion (discrete mathematics)|inversion]] table.

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==Similar concepts==

TwoSeveral similarrelated vectorsconstructions arehave inalso been put into use. One of them is often called inversion vector, e.g. by [[Wolfram Alpha]].

Two similar vectors are in use. One of them is often called inversion vector, e.g. by [[Wolfram Alpha]].

See also {{Section link|Inversion_(discrete_mathematics)|Inversion related vectors}}.

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==References==

{{Reflist|refs=

<ref name="lehmer">

{{Citation

| last=Lehmer

| first=D.H.

| title=Combinatorial Analysis

| auhtor-link=D. H. Lehmer

| titlechapter=Teaching combinatorial tricks to a computer

| series=Proceedings of Symposia in Applied Mathematics

| journal=Proc. Sympos. Appl. Math. Combinatorial Analysis, Amer. Math. Soc.

| auhtorauthor-link=D. H. Lehmer

| volume=10

| year=1960

| pages=179–193

| doi=https://doi.org/10.1090/psapm/010/0113289

| isbn=978-0-8218-1310-2

| mr=0113289

}}

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| last=Laisant

| first=Charles-Ange

| author-link= Charles-Ange Laisant

| title=Sur la numération factorielle, application aux permutations

| trans-title=On factorial numbering, application to permutations