lec19-more-counting - EECS 203 Winter 2007 Discrete...

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EECS 203, Winter 2007 Discrete Mathematics Lecture 19 More on counting March 15 Reading: Rosen [5.5]; Lehman [17] Useful references: A table complied by Bent Petersen: http://oregonstate.edu/ peterseb/mth355/docs/355f2001 counting.pdf . Eric Lehman and Tom Leighton’s lecture note at MIT: http://theory.lcs.mit.edu/ e lehman/mathcs.pdf . March 15 More on counting, Page 1
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19.1 Distributing objects into boxes Objects and boxes can be distinguishable (labeled) or indistinguishable (unlabeled). The number of distributing n objects to m boxes: n dist. objects, m dist. boxes: m n . n indist. objects, m dist. boxes: ( m + n - 1 m - 1 ) . n indist. objects, m indist. boxes: no closed form fomular The number of ways to partition n as sum of natural numbers: partition function p ( n ). March 15 More on counting, Page 2
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19.2 Stirling numbers of the second kind n dist. objects, m indist. boxes: m j =1 s ( n, j ) s ( n, j )= # when no empty box: Stirling number of the second type.
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