most recent 30 from http://mathoverflow.net 2013-05-22T23:41:22Z http://mathoverflow.net/feeds/user/4102 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/68567/number-of-partitions-of-a-number-on-a-combinatorial-bracelet Nemanja 2011-06-22T23:35:08Z 2011-06-23T15:40:39Z

<p>Suppose we have a <a href="http://en.wikipedia.org/wiki/Bracelet_(combinatorics)" rel="nofollow">combinatorial bracelet</a> composed of natural numbers. </p> <p>(Two bracelets are equivalent if you can get from one to the other via rotation or reflection.)</p> <p>What is the number of different bracelets whose elements sum up to a previously fixed natural number N?</p> <p>Also, are there any results if we add a constraint that the number of beads on the bracelet is always odd?</p> <p>P.S. Any good upper bounds are also helpful.</p> <p>(<strong>EDITED</strong> in the light of the comments below)</p>

http://mathoverflow.net/questions/15821/approximating-a-set-with-fixed-number-of-elements Nemanja 2010-02-19T16:31:48Z 2010-02-19T20:27:22Z

<p>I have a set <em>S</em> of real numbers, and I would like to create a new set <em>R</em> with exactly n real numbers (not necessarily from the set) that represent it best.</p> <p>What I mean by best?</p> <p>Well, I have query that asks for given point what is the closest point from S to that point, and when I ask same thing for set R I would like to have best fit to the real answers.</p> <blockquote> <p>To be specific, how do I minimize the <a href="http://en.wikipedia.org/wiki/Hausdorff%5Fdistance" rel="nofollow">Hausdoff distance</a> between <em>S</em> and <em>R</em>?</p> </blockquote> <p>I hope I've been clear enough in what i want. I've heard of mathoverflow, so I said to myself why wouldn't I ask for help there. </p> <p>Thank you in advance.</p> <p>(<strong>Edited</strong> in light of the comments below.)</p>

http://mathoverflow.net/questions/68567/number-of-partitions-of-a-number-on-a-combinatorial-bracelet/68621#68621 Nemanja 2011-06-23T16:50:56Z 2011-06-23T16:50:56Z

Following links give the answer to restriction to odd number of commas. <a href="http://oeis.org/search?q=12%2C23%2C34%2C63&amp;sort=&amp;language=english&amp;go=Search" rel="nofollow">oeis.org/&hellip;</a> <a href="http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&amp;id=pdf_1&amp;handle=euclid.pjm/1102711113" rel="nofollow">projecteuclid.org/DPubS/Repository/1.0/&hellip;</a>

http://mathoverflow.net/questions/68567/number-of-partitions-of-a-number-on-a-combinatorial-bracelet/68621#68621 Nemanja 2011-06-23T16:17:59Z 2011-06-23T16:17:59Z

Thank you for your explanation. Actually, I have just calculated answer for small values, as Gerry Myerson suggested, and got the (almost) bijection over the OEIS, but nevertheless your explanation is valuable.

http://mathoverflow.net/questions/68567/number-of-partitions-of-a-number-on-a-combinatorial-bracelet Nemanja 2011-06-23T12:37:43Z 2011-06-23T12:37:43Z

Yes, I meant positive integers. Sorry for not being clear. And yes, Gerry, that is the right definition of a bracelet.

http://mathoverflow.net/questions/15821/approximating-a-set-with-fixed-number-of-elements/15838#15838 Nemanja 2010-02-20T19:08:31Z 2010-02-20T19:08:31Z

you don't need even to check all n-choose-2 points, it is enough to move with an interval [ai..aj] so that d(ai,aj)&lt;=r and you only check (ai + aj) / 2

http://mathoverflow.net/questions/15821/approximating-a-set-with-fixed-number-of-elements/15838#15838 Nemanja 2010-02-20T10:48:40Z 2010-02-20T10:48:40Z

right, but i definitely wouldn't want to go trough the &quot;whole&quot; real line, so going through the input set would be the best way.

http://mathoverflow.net/questions/15821/approximating-a-set-with-fixed-number-of-elements/15838#15838 Nemanja 2010-02-20T04:46:52Z 2010-02-20T04:46:52Z

great. thank you. so by doing this i would get my error to be maximum r. But, if i don't restrict myself to choosing centers from the given set, i could get r/2, right? I could just chose from every ball (a0 - r, a0 + r), a0 + r/2 for my center and then I would get error of maximum r/2.

http://mathoverflow.net/questions/15821/approximating-a-set-with-fixed-number-of-elements/15823#15823 Nemanja 2010-02-19T17:15:13Z 2010-02-19T17:15:13Z

Thanks for Hausdorff metric. I don't get exactly what is the significance of my representation of a set ?

http://mathoverflow.net/questions/15821/approximating-a-set-with-fixed-number-of-elements Nemanja 2010-02-19T17:12:58Z 2010-02-19T17:12:58Z

Thank you for pointing me to Hausdorff distance. I think that this question would be precise enough: how can i find a set R with n or less elements that has the smallest Hausdorff distance to set S. S is a finite set of real numbers.

http://mathoverflow.net/questions/15821/approximating-a-set-with-fixed-number-of-elements Nemanja 2010-02-19T17:01:47Z 2010-02-19T17:01:47Z

Yes, by one dimensional set I've meant subset of the real numbers. And yes, standard distance function. I am trying to minimize average error e.g. if my answer on set R is x and answer on set S would be y, I am trying to minimize average value of |x - y|