AlanH
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 Jan12 comment How to approach this problem of combinatorics Nevermind! I was thinking for the general case. Jan12 comment How to approach this problem of combinatorics Shouldn't it be 144? I believe you're missing a 2. Jan12 accepted How to approach this problem of combinatorics Jan11 comment How to approach this problem of combinatorics So I shouldn't even be caring about what the actual products are? If I'm reading what you wrote correctly, this is almost like how many combinations I can make of 1 apple, 2 oranges, 2 pears, 1 kiwi, and 3 mangoes? Jan11 asked How to approach this problem of combinatorics Jan6 accepted Proof involving Stirling numbers of the second kind Jan6 awarded Commentator Jan6 comment Proof involving Stirling numbers of the second kind @BrianM.Scott Maybe it's assumed for all positive integers greater than equal to $k$? Jan5 comment Proof involving Stirling numbers of the second kind @BrianM.Scott Yeah, I'm looking at it right now and it says, in italics, all positive integers x. Jan5 asked Proof involving Stirling numbers of the second kind Jan3 comment prove that $\text{rank}(AB)\ge\text{rank}(A)+\text{rank}(B)-n.$ Have you tried working out an example? Try a few by hand and see if you can generalize it. Or you can try showing it by contradiction; though I always feel direct proofs are much more clear. Jan2 accepted How to simplify this equality (factorials)? Jan2 asked How to simplify this equality (factorials)? Dec28 accepted Pigeon-hole Principle: Does this proof have a typo? Dec28 accepted If an integer is divisible by 8 and 15, then the integer also must be divisible by which of the following? Dec28 accepted How is this a property of Pascal's triangle? Dec26 awarded Analytical Dec26 asked How is this a property of Pascal's triangle? Dec20 comment If an integer is divisible by 8 and 15, then the integer also must be divisible by which of the following? Ah! I figured it out just now. Thank you Dec20 comment If an integer is divisible by 8 and 15, then the integer also must be divisible by which of the following? What else does it imply? (I actually thought about it, but I'm quite hesitant to state what I think).