Re^2: Combinatorics problem. (Updated with more info.)

++ oiskuu i suspected that the answer had to be in the triangle.. congrats!

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Comment on Re^2: Combinatorics problem. (Updated with more info.) Download Code

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Re^3: Combinatorics problem. (Updated with more info.) by danaj (Friar) on Dec 11, 2015 at 23:06 UTC
From DLMF or MathWorld we see the number of restricted compositions is binomial(n-1,m-1). So: `perl -Mntheory=:all -E 'say binomial(12-1,7-1)' 462` [download] Basically the same with Math::Pari or Pari/GP. Chinn and Heubach (2003) and Opdyke (2008) have interesting info relating restricted compositions to Pascal's triangle. Edit: There's also some interesting but scattered info on OEISWiki, including the idea of encoding the compositions as RLE on binary. For generating the sequences, Kelleher's paper is a great reference.	[reply] [d/l]

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Re^3: Combinatorics problem. (Updated with more info.)
by danaj (Friar) on Dec 11, 2015 at 23:06 UTC

From DLMF or MathWorld we see the number of restricted compositions is binomial(n-1,m-1). So:

perl -Mntheory=:all -E 'say binomial(12-1,7-1)'
462
[download]

Basically the same with Math::Pari or Pari/GP.

Chinn and Heubach (2003) and Opdyke (2008) have interesting info relating restricted compositions to Pascal's triangle.

Edit: There's also some interesting but scattered info on OEISWiki, including the idea of encoding the compositions as RLE on binary. For generating the sequences, Kelleher's paper is a great reference.

[reply]
[d/l]