OKlibrary  0.2.1.6
OK_XSZ_min_degree.hpp
Go to the documentation of this file.
00001 // Oliver Kullmann, 29.8.2009 (Swansea)
00002 
00252 sp_uhitdef3(i,j) := block([BF : musatd2(3)[2], C1, C2],
00253   C1 : listify(BF)[i], C2 : listify(BF)[j],
00254   union(setdifference(BF, {C1,C2}), {adjoin(4,C1), adjoin(-4,C1), adjoin(4,C2), adjoin(-4,C2)}))$
00255 L : create_list(sp_uhitdef3(i,j), i,1,4,j,i+1,5)$
00256 check(F) := not emptyp(check_hitting_nsing_def(F)) and not full_var_csp(F)$
00257 every_s(check,L);
00258 (%i32) map(second,classify_candidates_uhit_def(L));
00259   [1,1,1,9,7,7,1,7,1,1]
00260     \endverbatim
00261     So they are all already in the catalogue. </li>
00262     <li> In the hitting catalogue of the OKlibrary we have 7 different
00263     examples of such F:
00264     \verbatim
00265 H3 : all_uhit_def(3)$
00266 H3n : sublist(H3, lambda([F], not full_var_csp(F)));
00267  [{{-4,-3},{-4,-1,2,3},{-4,1,2,3},{-3,-2,4},{-2,-1,3},{-2,1,3},{2,4}},
00268  {{-4,-3},{-4,-1,2,3},{-4,1,3},{-3,-2,-1,4},{-2,-1,3},{-2,1,4},{2,4}},
00269  {{-4,-3},{-4,2,3},{-3,-2,1,4},{-3,-1,4},{-2,3},{-1,2,3,4},{1,2,4}},
00270  {{-4,-3,-2},{-4,2},{-3,-1,4},{-3,1,4},{-2,-1,3},{-2,1,3},{2,3,4}},
00271  {{-4,-3,-2,-1},{-4,1,2,3},{-3,-2,-1,4},{-3,1},{-2,3},{-1,2},{1,2,3,4}},
00272  {{-5,-4,-2,-1},{-5,-4,-2,1},{-5,-2,-1,4},{-5,-2,1,4},{-5,2,3},{-3,-2,5},{-3,2},{3,5}},
00273  {{-5,-4},{-5,-3,4},{-4,-2,-1,3,5},{-4,-2,1,3,5},{-4,-1,2,3,5},{-4,1,2,3,5},{-3,5},{3,4}}]
00274 map(second,classify_candidates_uhit_def(H3n));
00275  [1,3,4,7,9,4,6]
00276     \endverbatim
00277     </li>
00278     <li> So XSZ's examples have indices 1, 4, 5 in H3n. while indices 2,3,6,7
00279     contain new examples; these are
00280     \verbatim
00281  {{-4,-3},{-4,-1,2,3},{-4,1,3},{-3,-2,-1,4},{-2,-1,3},{-2,1,4},{2,4}},
00282  {{-4,-3},{-4,2,3},{-3,-2,1,4},{-3,-1,4},{-2,3},{-1,2,3,4},{1,2,4}},
00283  {{-5,-4,-2,-1},{-5,-4,-2,1},{-5,-2,-1,4},{-5,-2,1,4},{-5,2,3},{-3,-2,5},{-3,2},{3,5}},
00284  {{-5,-4},{-5,-3,4},{-4,-2,-1,3,5},{-4,-2,1,3,5},{-4,-1,2,3,5},{-4,1,2,3,5},{-3,5},{3,4}}]
00285      \endverbatim
00286     </li>
00287     <li> If the above is everything, then actually N(3) would be 7. </li>
00288    </ol>
00289    </li>
00290    <li> Before Lemma 1, everything should already be in the report. </li>
00291   </ul>
00292 
00293 */
00294