Combinatorics (Fall 2010)/Basic enumeration: Difference between revisions

Revision as of 02:51, 8 July 2010

Elements of [math]\displaystyle{ N }[/math]	Elements of [math]\displaystyle{ M }[/math]	Any [math]\displaystyle{ f }[/math]	Injective (1-1) [math]\displaystyle{ f }[/math]	Surjective (on-to) [math]\displaystyle{ f }[/math]
distinguishable	distinguishable	[math]\displaystyle{ m^n }[/math]
indistinguishable	distinguishable		[math]\displaystyle{ {m\choose n} }[/math]
distinguishable	indistinguishable
indistinguishable	indistinguishable

@@ Line 6: / Line 6: @@
 == The twelvfold way ==
+{|border="2"  cellspacing="4" cellpadding="3" rules="all" style="margin:1em 1em 1em 0; border:solid 1px #AAAAAA; border-collapse:collapse;empty-cells:show;"
+|-
+|bgcolor="#A7C1F2" | Elements of <math>N</math>
+|bgcolor="#A7C1F2" | Elements of <math>M</math>
+|bgcolor="#A7C1F2" | Any <math>f</math>
+|bgcolor="#A7C1F2" | Injective (1-1) <math>f</math>
+|bgcolor="#A7C1F2" | Surjective (on-to) <math>f</math>
+|-
+| distinguishable
+| distinguishable
+| <math>m^n</math>
+|
+|
+|-
+| indistinguishable
+| distinguishable
+|
+|<math>{m\choose n}</math>
+|
+|-
+| distinguishable
+| indistinguishable
+|
+|
+|
+|-
+| indistinguishable
+| indistinguishable
+|
+|
+|
+|}