Path: news.mathworks.com!not-for-mail From: <HIDDEN> Newsgroups: comp.soft-sys.matlab Subject: Re: how to generate all vectors of length n with entries are 0's or 1's then sum over Date: Tue, 13 Jul 2010 19:05:21 +0000 (UTC) Organization: The MathWorks, Inc. Lines: 39 Message-ID: <i1iddh$iq6$1@fred.mathworks.com> References: <i1iafp$6v7$1@fred.mathworks.com> Reply-To: <HIDDEN> NNTP-Posting-Host: webapp-05-blr.mathworks.com Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit X-Trace: fred.mathworks.com 1279047921 19270 172.30.248.35 (13 Jul 2010 19:05:21 GMT) X-Complaints-To: news@mathworks.com NNTP-Posting-Date: Tue, 13 Jul 2010 19:05:21 +0000 (UTC) X-Newsreader: MATLAB Central Newsreader 1187260 Xref: news.mathworks.com comp.soft-sys.matlab:652801 "yang " <macmaster_egypt@yahoogroups.com> wrote in message <i1iafp$6v7$1@fred.mathworks.com>... > Hi, > I need your help for this problem, please. > > \mathop {\sum {...\sum }}\limits_{z_r \in {Q_{2}^{*}}} such that > > Q_{2}^{*}=\{(z_1,...,z_r):z_{j}=0,1,\sum_{j=1}^{r}z_{j}=\ell\}, where \ell = 0, 1, . . . , r. > > For example. If r=3, \ell=1; then we are looking for triples with elements 0's or 1's and sum to 1 i.e. Q_{2}^{*}=\{(0,0,1),(0,1,0),(1,0,0)\}. So we would like to sum over theses z_r's. > > I appreciate your help. > Adam - - - - - - - - If I interpret your question correctly, for r = 5 and ell = 3, you first want all sequences of five 0's or 1's whose sum is 3: 0 0 1 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 1 0 1 0 0 1 1 1 0 1 0 1 1 0 1 1 0 1 1 0 0 1 1 1 0 1 0 1 1 1 0 0 Next you want the sum of each of these columns. Is that right? You don't need matlab for that trivial problem. The answer is always (r-1)!/(ell-1)!/(r-ell)! for each column. In the above case this is 4!/2!/2! = 6 which is clearly correct. Or, if you want the sum over all elements of all sequences, it would be r!/(ell-1)!/(r-ell)! Roger Stafford