9716

Set Partitions Match Restricted Growth Functions

Set partitions of can be matched to restricted growth functions . Each entry of such a function (or -vector) is at most one more than the maximum of the preceding entries.
The following explains the matching.
Suppose the partition is . We write this more compactly as .
Suppose the blocks are in order of their least element. In this example those elements are and the blocks are in order.
To construct the restricted growth function, put below the indices given by block : . Put below the indices given by block : . Finally put below the indices given by block : . Then the restricted growth function is .
To go the other way, reverse the process. For example, if the growth function is , then block is because those are the indices for . Block is and block is . The blocks are ordered by least element: .

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

D. Stanton and D. White, Constructive Combinatorics, New York: Springer–Verlag, 1986.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+