Stars and bars (combinatorics): Difference between revisions

Revision as of 10:05, 5 May 2021

Revision as of 20:32, 30 May 2021

Line 1:

In the context of [[combinatorial mathematics]], '''stars and bars''' (also called "sticks and stones"<ref>{{Cite book|last=Batterson|first=J|title=Competition Math for Middle School|publisher=Art of Problem Solving}}</ref> and "balls and bars" <ref>{{cite book|last1=Flajolet|first1=Philippe|last2=Sedgewick|first2=Robert|date=June 26, 2009|title=Analytic Combinatorics|publisher=Cambridge University Press|isbn = 978-0-521-89806-5}}</ref>) is a graphical aid for deriving certain [[combinatorial]] theorems. It was popularized by [[William Feller]] in his classic book on [[probability]]. It can be used to solve many simple [[combinatorial enumeration|counting problems]], such as how many ways there are to put ''n'' indistinguishable balls into ''k'' distinguishable bins.<ref>{{cite book |last=Feller |first=William |author-link=William Feller |year=1950 |title=An Introduction to Probability Theory and Its Applications |publisher=Wiley |volume=1 |edition=2nd}}</ref>

==Statements of theorems==