comb: Calculate the combinadic

In MichaelHoltonPrice/yada: Yet Another Demographic Analysis package

Description

[yada::comb], [yada::dual] [yada::elem], [yada::elem_to_index], and [yada::largest_V] together implement combinadics as described in the following document (see also details):

James McCaffrey – Generating the mth Lexicographical Element of a Mathematical Combination

Indexing begins from 0, not 1.

Usage

comb(m, N, k)

Arguments

m	The lexical index of each unique choice (starting from 0)
N	The number of unique things
k	The number of things to choose out of N total things
c	The combinadic (a vector; see details)

Details

Consider a set of N things of which k unique ones are chosen. The number of unique sets of things that can be chosen is choose(N,k). For example, if N=5 and k=3 there are choose(5,3) = 10 unique such sets. Adopting lexigraphic ordering starting at 0, the combinadic (comb), dual, and element (elem) are:

m comb dual elem 0 210 9 012 1 310 8 013 2 320 7 014 3 321 6 023 4 410 5 024 5 420 4 034 6 421 3 123 7 430 2 124 8 431 1 134 9 432 0 234

If the lexical index, m, is 2, the corresponding element with N=5 and k=3 is:

e <- elem(2,5,3) print(e) [1] 0 1 4

If the element is 421, the corresponding lexical index is:

m <- elem_to_index(c(1,2,3),5) print(m) [1] 6

Value

The combinadic (a vector; see details)

MichaelHoltonPrice/yada documentation built on Sept. 19, 2021, 11:27 p.m.