Description Usage Arguments Details Author(s)
Implementation of combinadic-related functions as described here:
James McCaffrey – Generating the mth Lexicographical Element of a Mathematical Combination
Indexing begins from 0, not 1.
1 | comb(m, N, k)
|
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) |
d |
The dual(see details) |
e |
The element (a vector; see 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 <- elemToIndex(c(1,2,3),5) print(m) [1] 6
Michael Holton Price <MichaelHoltonPrice@gmail.com>
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