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Laws
We are already in the position to guess the truth formula. What happens for a three variables truism ?

$$ X + Y + Z + XY + YZ + XZ + ZYZ$$

Labelled Issues
go to Labelled Issues Page When taking into account more sorts, there is a rule of thumb : For each exclamation mark that occurs in a combinatorial formula, there is one different sort that lies behind.


 * Sum & Product,
 * Composition,
 * Constants,
 * Sampling,
 * Counters,
 * Combs

Unlabelled Issues
go to Unlabelled Issues


 * String factories,
 * Short strings P.I.E.,
 * Goulden-Jackson,
 * Soup and Croutons

Polya Issues
 go to Polya Issues


 * MathStackExchange problems
 * Orbits and Burnside Lemma
 * Colored permutations
 * Double permutations
 * Stirling - exact # of colors
 * The Cube

=More=

Studies

 * Notes on Species


 * Transitivity - Stick-Stuck, The Spectrum, Carmichael


 * Coordinates - Introducing, Labelling the Fano Plane


 * Pointing - Fano', Chvatal', Prism', Cube'


 * Sampling


 * Parantheses Catalan Numbers, Parantheses, Seven Trees in One, Divergent Series


 * Goulden Jackson Each object is a multi-sort one

Appendix

 * Formulas - Essentials from BLL book


 * Configurations in Fano Plane


 * Subtraction Tables


 * Fibonacci as types of labeled structures


 * Alexander's Paradoxes


 * Bob Proctor - Let's Expand Rota's Twelvefold Way For Counting Partitions!


 * Formal Languages and Automata - Counting strings in Peter Linz book


 * Marks Tables


 * Reviews


 * Substructures extra

Stuff
https://en.wikipedia.org/wiki/Help:Wiki_markup

https://en.wikipedia.org/wiki/Help:Displaying_a_formula

https://www.math-linux.com/latex-26/faq/latex-faq/article/horizontal-and-vertical-curly-braces-left-right-underbrace-and-overbrace

https://latex.wikia.org/wiki/Main_page

Math Symbols

Sandbox

ln how manyways can we distribute 7 apples and 6 oranges among 4 children so that each child gets at least one apple.

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

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

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

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

https://math.stackexchange.com/questions/1170811/there-are-5-students-must-form-3-teams-and-every-team-must-have-2-students-in-c?rq=1

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