## FANDOM

28 Pages

For this subject matter, definitions and even formal calculations and heuristic deductions seem to me often more important than complete proofs. Polya, 1937

Kenneth P. Bogart, · 2004 ·

# Why e.g.f.'s ? Edit

A G.F. is always produced by an e.g.f. When aggregating two solids, the exponential stuff vanishes like in

$3! {x^3 \over 3!} . 7! {x^7 \over 7!} = 10! {x^{10} \over 10!}$ that becomes $x^3 . x^7 = x^{10}$

The aggregate operation rule is $3! * 7! = (3+7)!$ and it is discarded.

## Current work Edit

Goulden-Jackson: N(x)=E(x+1)
Grammars - Unambiguous grammars are combinatorial species.
Exclusion: $F(X+Y-XYX + XYXYX)$

## Welcome to Species : the ArticleEdit

Combinatorial species at work - the article, original research !

## OperationsEdit

Summation: $F(X) + G(X) = F(X) + G(Y)$
Constants and the double reading of F(A,X)
Composition Wreath product, Plethistic substitution
Differentiation : $F'$ and point stabilizers: $Chvatal', \ Prism', \ Cube'$, multisort differentiation, stick-k-stuck-n
Sampling: generalized differentiation
Multisorting: F(X+Y)
Merging sorts - how un-coloring does or not affect cardinality
Weighted species = the t counter
Functorial Composition - card decks, shoes, $\bbox[border:1px solid black]{^AS}$
Hypergeometric: The sixth ball is white

Divergent series or linear species.

More examples Sudoku

## Appendix Edit

Subtraction : 6-2, 4-2

Fano plane : subspecies of Fano Plane

https://oeis.org/A011971 to see

Solomon, L. (1967), "The Burnside algebra of a finite group", J. Comb. Theory, 1: 603–615

## StuffEdit

Let $A_n$ be the number of such sequences ending in A, and $B_n$ be the number of such sequences ending in B. We count the empty string in both.

$\bbox[1px,border:2px solid #00A000]{^AS}$

$\bbox[5px,border:2px solid #00A000]{ \begin{gather} H_X(N, M) = \frac{N! \times M!}{24} \\ \times \left({6\brace N} {8\brace M} + 6 {3\brace N} {2\brace M} + 3 {4\brace N} {4\brace M} + 8 {2\brace N} {4\brace M} + 6 {3\brace N} {4\brace M}\right). \end{gather}}$

$\sum_{S \subset N \setminus \{i\}} {|S|!(n-|S|-1)!}=n!$

$\begin{eqnarray*} \underbrace{** }_{ k_1 \text{ stars}} \mid \underbrace{*** }_{ k_2 \text{ stars}} \mid \cdots \mid \underbrace{*}_{ k_n \text{ stars}} \\ \sum_{i=1}^{n} k_i=k. \end{eqnarray*}$

## ExtraEdit

Dytran-threetran will it ever find its place ?

## Latest ActivityEdit

• Grammars
edited by Boyku  Edited the section: SLUMGULLION
• Weighted species
edited by Boyku  Edited the section: The game of Clue involves 6 suspects, 6 weapons, and 9 rooms (Ross)
• Functorial Composition
edited by Boyku  Summary: ‎an urn contains six ball of each of the three colors: red, blue, and green:
• Functorial Composition
edited by Boyku  Edited the section: Two pair is 123552
• Home
edited by Boyku  Edited the section: Operations
• Hands and Decks
edited by Boyku  Edited the section: Two pair is 123552
• Hands and Decks
edited by Boyku  Edited the section: Poker hands
• Hands and Decks
edited by Boyku  Edited the section: Choose one - 52
• Hands and Decks
edited by Boyku  Edited the section: Two pair is 123552
• Goulden-Jackson
edited by Boyku  Edited the section: The number of sequences of length 10 that can be formed with 5 unique digits containing two of each where no two adjacent elements are alike

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