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

Fruits 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

Alexander's paradoxes Train, cafeteria

Divergent series or linear species.

More examples Sudoku

Appendix Edit

Surjections

Fibonacci

Tables

Reviews

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} $

https://math.stackexchange.com/questions/2828924/coloring-cube-sides-and-vertices

$ \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}} $

https://math.stackexchange.com/questions/2853626/is-it-true-that-sum-s-subset-n-setminus-i-sn-s-1-n-where

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

https://math.stackexchange.com/questions/2855911/combinatorial-proof-of-negative-binomial-identity

$ \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

Sandbox

Math symbols

Dytran-threetran will it ever find its place ?

https://math.stackexchange.com/questions/2912210/another-beauty-hidden-in-a-simple-triangle-3

Latest ActivityEdit



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