http://openproblemgarden.org/op/covering_designs Comments for "Combinatorial covering designs" en http://openproblemgarden.org/op/covering_designs <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/gordon_d_m">Gordon</a>; <a href="/category/mills_w_h">Mills</a>; <a href="/category/rodl_v">Rödl</a>; <a href="/category/schonheim_j">Schönheim</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/combinatorics">Combinatorics</a> » <a href="/category/designs">Designs</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <p>A <img class="teximage" src="/files/tex/56c6ecfd1aa60a2d9b08685a6873e02051db1064.png" alt="$ (v, k, t) $" /> <i>covering design</i>, or <i>covering</i>, is a family of <img class="teximage" src="/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png" alt="$ k $" />-subsets, called <i>blocks</i>, chosen from a <img class="teximage" src="/files/tex/96cbd9a16c6a5eab03815b093b08f3b2db614e9a.png" alt="$ v $" />-set, such that each <img class="teximage" src="/files/tex/4761b031c89840e8cd2cda5b53fbc90c308530f3.png" alt="$ t $" />-subset is contained in at least one of the blocks. The number of blocks is the covering’s <i>size</i>, and the minimum size of such a covering is denoted by <img class="teximage" src="/files/tex/0b10d6aba96c527ae8e7c843d733ebfde1b2c606.png" alt="$ C(v, k, t) $" />.</p> <div class="envtheorem"><b>Problem</b>&nbsp;&nbsp; Find a closed form, recurrence, or better bounds for <img class="teximage" src="/files/tex/57e0c3d8ecd38c439689b3e42371c262cce1bab2.png" alt="$ C(v,k,t) $" />. Find a procedure for constructing minimal coverings. </div> </tr></td> </table> </td> </tr> </table> Gordon, D.M. Mills, W.H. Rödl, V. Schönheim, J. recreational mathematics Combinatorics Designs http://openproblemgarden.org/op/covering_designs#comment Fri, 11 Apr 2008 02:48:32 +0200 Pseudonym 762 at http://openproblemgarden.org