Hi guys just a quick questions What are the real life application of catalan numbers? Thanks a lot!
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5$\begingroup$ They are useful when you go shopping in Catalonia. I voted to close. $\endgroup$– AngeloCommented May 15, 2012 at 14:24
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$\begingroup$ I voted to close, but am now about to give an answer. I don't know how to retract a close vote... $\endgroup$– Igor RivinCommented May 15, 2012 at 15:12
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$\begingroup$ The faq explains how such questions are not appropriate for mathoverflow. There are other fora where you will have better luck. $\endgroup$– Gjergji ZaimiCommented May 15, 2012 at 15:17
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$\begingroup$ Sorry I admit forgetting to check the FAQ I'll be sure to check it next time then Thanks for the help anw $\endgroup$– user23731Commented May 15, 2012 at 15:49
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2 Answers
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In all seriousness, this type of enumerative combinatorics is very useful e.g. in figuring out expected running time for computer programs. An example involving Catalan numbers (which may seem a little contrived, but I think things like this probably do really come up) is: count how many times you go through the inner loop, i.e. how many times you print "hello world", in:
for $i_1=0$ to $1$
for $i_2=i_1$ to $2$
for $i_3=i_2$ to $3$
...
for $i_n = i_{n-1}$ to $n$
print "hello world"
answered May 15, 2012 at 14:39
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$\begingroup$ You're welcome. I wonder about these things too. $\endgroup$ Commented May 17, 2012 at 21:25
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This is discussed at great length in:
"Catalan numbers with applications" by Thomas Koshy. The main application seems to be to make money for the publisher (the book is insanely expensive), but google books has extracts.
answered May 15, 2012 at 15:13