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数学

Discovery

Andrius Kulikauskas

  • ms@ms.lt
  • +370 607 27 665
  • My work is in the Public Domain for all to share freely.

Lietuvių kalba

Introduction E9F5FC

Understandable FFFFFF

Questions FFFFC0

Notes EEEEEE

Software

I want to list and generate the basic combinatorial objects.

Stanley Enumerative Combinatorics

  • Volume I
  • Volume II: Table of Contents
  • The Twelvefold Way
  • Permutations
  • Sieve methods - Inclusion Exclusion
  • Partially ordered sets
  • Rational generating functions
  • Trees and the Composition of Generating Functions
  • Algebraic, D-Finite, and Noncommutative Generating Functions
  • Symmetric functions

The Twelvefold Way f:N->X two sets

  • f is arbitrary (no restriction)
  • f is injective (one-to-one)
  • f is surjective (onto)

And regarding the elements of N and X as "distinguishable" or "indistinguishable".

{$(x)_{n}=x(x-1)(x-2)...(x-n+1)$}

{$S(n,k)$} is the number of partitions of an n-set into k-blocks. It is called a Stirling number of the second kind.

Objects


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Puslapis paskutinį kartą pakeistas 2018 sausio 07 d., 18:57
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