Wikipedia:Reference desk/Archives/Mathematics/2011 December 24

= December 24 =

Duck question?
How many ducks(minimum) is required for following arrangement: 1.there should be 2 ducks in front. 2.there should be 2 ducks in back 3.there should be a duck between two ducks.

dear frens,pls quote your logic in coming to conclusion


 * -Regards, — Preceding unsigned comment added by Abcappu (talk • contribs) 11:58, 24 December 2011 (UTC)


 * The meaning of "there should be a duck between two ducks" is not clear. Looie496 (talk) 15:40, 24 December 2011 (UTC)
 * Google search "two ducks in front behind between" Kittybrewster  &#9742;  15:47, 24 December 2011 (UTC)

Methinks it is retarded to say "It's amazing how many people got this one wrong" when the question as posed is ambiguous (Yahoo! Answers). Here's what I had pictured:

Duck Duck

Duck

Duck Duck

Didn't realize it was supposed to be single file line. --COVIZAPIBETEFOKY (talk) 16:33, 24 December 2011 (UTC)


 * The formulation posted here is particularly ambiguous and I wouldn't have thought it allowed three ducks in a row. "2 ducks in front" sounds like they should be equally in front when it isn't said they just both have to be in front of another duck. Many versions elsewhere are less ambiguous but still open to some interpretation. PrimeHunter (talk) 15:31, 25 December 2011 (UTC)


 * I see it as a single file:

DUCK DUCK DUCK


 * The first two are in front, the last two are in back, and the center duck is between two ducks. StuRat (talk) 15:44, 25 December 2011 (UTC)


 * StuRat: I linked to a page where that was explained already. --COVIZAPIBETEFOKY (talk) 17:49, 25 December 2011 (UTC)


 * Yes, but it also gave the wrong answer several times, and the right answer is quite short, so why not put it right here ? StuRat (talk) 22:36, 30 December 2011 (UTC)


 * This question is as daft as the ducks that feature in it. 86.179.114.20 (talk) 21:47, 25 December 2011 (UTC)

number of jordan decomposition
let {A} be a set of nxn matrices over F, and let the characteristic polynomial of each element be $$(x-a_1)^{b_1}...(x-a_m)^{b_m}$$.

Is there a formula for the amount of differnet possible jordan forms for elements of {A}?

If not, is there somewhere in the internet where I can let a computer do this? (enter different polynomials and get the answer without actually doing that work?) --84.228.160.190 (talk) 19:37, 24 December 2011 (UTC)
 * If A is given then the Jordan normal form is unique so the formula is 1. I think what you meant is that the characteristic polynomial is given and you want the number of possible JNF's for matrices with that polynomial. If the polynomial has the form (x-a)b then I believe the answer is P(b)=the number of integer partitions of b. In the general case it would be the product of P(bi) where bi runs over the exponents in the factorization.--RDBury (talk) 20:58, 24 December 2011 (UTC)
 * Actually the Jordan form of a given A is unique, up to permutations of its Jordan blocks. --pm a 10:04, 25 December 2011 (UTC)
 * Why is it true?--77.124.235.177 (talk) 19:05, 26 December 2011 (UTC)