User tmy1018 - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T20:24:06Z http://mathoverflow.net/feeds/user/10028 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/90907/the-relationship-between-stirling-number-of-the-second-kind-and-the-polylogarithm The relationship between Stirling number of the second kind and the polylogarithm tmy1018 2012-03-11T15:01:12Z 2012-03-11T19:22:15Z <p>It is shown here on <a href="http://mathworld.wolfram.com/StirlingNumberoftheSecondKind.html" rel="nofollow">Mathworld's page on Stirling number of the second kind</a> that </p> <p>$$\sum_{k=1}^n S(n,k) (k-1)! z^k = (-1)^n \text{Li}_{1-n}(1+\frac{1}{z})$$</p> <p>where $S(n,k)$ is Stirling number of the second kind and $\text{Li}_{1-n}$ is the polylogarithm.</p> <p>Can somebody provide me some reference on where this identity came from? It isn't shown on Mathworld's page.</p> http://mathoverflow.net/questions/85038/cover-a-line-segment-randomly-with-smaller-line-segments/86786#86786 Answer by tmy1018 for Cover a line segment randomly with smaller line segments tmy1018 2012-01-27T03:26:46Z 2012-01-27T03:26:46Z <p>This problem can actually be solved using the exact same method as Chapter 4 of Solomon's geometric probability.</p> http://mathoverflow.net/questions/85038/cover-a-line-segment-randomly-with-smaller-line-segments Cover a line segment randomly with smaller line segments tmy1018 2012-01-06T08:50:54Z 2012-01-27T03:26:46Z <p>Covering a circle randomly with arcs has been well studied in the past (<a href="http://books.google.com.hk/books/about/Geometric_Probability.html?id=tY8cAZFklIEC" rel="nofollow">Geometric Probability - Solomon</a>).</p> <p>But the problem when the circle is changed to a line segment doesn't seem to have been studied before.</p> <p>I'd like to know if there's any work out there who already obtained the probability distribution of the number and the length of the connected line segments that you get when randomly covering a line segment with another set of shorter segments, which may all be of equal length or have some kind of distribution.</p> <p>Thanks!</p> http://mathoverflow.net/questions/100788/degeneracy-of-the-analytic-center-of-a-set-of-linear-inequalities Comment by tmy1018 tmy1018 2012-06-28T02:49:45Z 2012-06-28T02:49:45Z When you have a set of inequalities $$\begin{cases} x_1+x_2+x_3+x_4\leq 4\\ 3x_1+x_2+x_3+x_4\leq 6 \end{cases}$$ then it seems that the analytic center should be degenerat http://mathoverflow.net/questions/92242/a-discrete-optimization-problem-involving-binomial-coefficients Comment by tmy1018 tmy1018 2012-03-26T15:31:06Z 2012-03-26T15:31:06Z Sorry, I forgot to write the constraints on $a_1,a_2,...,a_k$, it has been corrected now. http://mathoverflow.net/questions/92015/how-to-get-a-bootstrap-confidence-interval-for-the-mle-for-the-parameter-of-a-con Comment by tmy1018 tmy1018 2012-03-23T16:06:23Z 2012-03-23T16:06:23Z @BR Could you please point me to some other references, I'm afraid I can't obtain a copy of the work they referred to there. http://mathoverflow.net/questions/89872/an-enumeration-problem-arising-from-dna-sequencing-statistics/89920#89920 Comment by tmy1018 tmy1018 2012-03-01T06:16:19Z 2012-03-01T06:16:19Z Sorry, it should have been 144, I just fixed it. http://mathoverflow.net/questions/89364/a-good-bound-or-an-asymptotic-formula-for-a-sum-involving-binomial-coefficients Comment by tmy1018 tmy1018 2012-02-25T06:28:00Z 2012-02-25T06:28:00Z I edited this a little by adding some restrictions on the variables. http://mathoverflow.net/questions/85038/cover-a-line-segment-randomly-with-smaller-line-segments Comment by tmy1018 tmy1018 2012-01-10T01:20:18Z 2012-01-10T01:20:18Z @fedja The problem is can be described like this: if smaller line segments are randomly picked from a longer line segment, what's the distribution of the number of connected &quot;contigs&quot; that consist of overlapping line segments and what's the distribution of the number of gaps? You can see Chapter 6 in in Solomon's Geometric Probability. http://mathoverflow.net/questions/85038/cover-a-line-segment-randomly-with-smaller-line-segments Comment by tmy1018 tmy1018 2012-01-08T03:14:33Z 2012-01-08T03:14:33Z @Anthony The problem I'm talking about is [DNA sequencing](<a href="http://en.wikipedia.org/wiki/DNA_sequencing" rel="nofollow">en.wikipedia.org/wiki/DNA_sequencing</a>)