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File:Combinations with repetition; 5 multichoose 3.svg

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Original file(SVG file, nominally 626 × 685 pixels, file size: 701 KB)

Description

There's a bijection between

  • the k-element multisets with elements from an n-element set    (k-combinations of n elements with repetitions)
  • and the k-element subsets of an n+k−1-element set    (k-combinations of n+k−1 elements without repetitions).

This file shows the bijection between

  • the 3-element multisets with elements from     (right side)
  • and the 3-element subsets of a 7-element set    (left side).

The first line represents the following correspondence between a 7-tuple, a 5-tuple and a 3-element multiset:

(1,1,1,0,0,0,0) ≙ (3,0,0,0,0) ≙ {1,1,1}

The scetches between 7- and 5-tuples are meant to be intuitive, and do not represent mathematical objects.

Date
Source Own work
Author Watchduck.svg Watchduck (a.k.a. Tilman Piesk)
Other versions

Printable version: File:Combinations with repetition; 5 multichoose 3.pdf

Related files

  without repetition with repetition
Variations Variations without repetition; 5 choose 3.svg

Variations with repetition; 5 multichoose 3; grouped.svg



Combinations Combinations without repetition; 5 choose 3.svg

Combinations with repetition; 5 multichoose 3; grouped.svg



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Date/TimeThumbnailDimensionsUserComment
current18:49, 26 April 2011Thumbnail for version as of 18:49, 26 April 2011626 × 685 (701 KB)Watchducktext into objects
17:45, 26 April 2011Thumbnail for version as of 17:45, 26 April 2011626 × 685 (738 KB)Watchduck{{Information |Description= |Source={{own}} |Date=2011 |Author= Lipedia |Permission= |other_versions= }} == Licensing: == {{self|GFDL|cc-by-3.0}} Category:Combinatorics
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