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Book: MathInterpretations


Organize the interpretations of various combinatorial objects



The factoring (number of simplexes n choose k - dependent simplex) x (number of flags on k - independent Euclidean) x (number of flags on n-k - independent Euclidean) = (number of flags on n)

The combinatorial interpretation of n-choose-k counts placements = "external arrangements" n! x...x (n-k+1)! and then divides by the redundancies = "internal arrangements" k! Thus it relates external and internal (within subsystem).

Conjugation gives the ways of relabeling, renaming. For example, (132)(12)(123) relables 1 as 2 and 2 as 3 in (12) to get (23).


I want to list and generate the basic combinatorial objects.

Stanley Enumerative Combinatorics

The Twelvefold Way f:N->X two sets

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.

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Puslapis paskutinį kartą pakeistas 2020 sausio 27 d., 19:49