Counting unlabelled topologies and transitive relations
... their numbers up to 12 points. In this paper, we extend the counts to 15 or 16 points. We defer to [3] for historical survey, and only give enough background to precisely define the objects we are counting. We consider only directed graphs (digraphs) that do not have multiple edges but may have up t ...
... their numbers up to 12 points. In this paper, we extend the counts to 15 or 16 points. We defer to [3] for historical survey, and only give enough background to precisely define the objects we are counting. We consider only directed graphs (digraphs) that do not have multiple edges but may have up t ...
Olymon for February, 2009 - Department of Mathematics
... Solution. Suppose without loss of generality that AB > AC. If M is the midpoint of BC, since BG : GC = AB : AC, BG > GC so that G lies between M and C and A lies between E and F . Let P be the intersection of DF and EG. Observe that D is the midpoint of the arc BC and that AD ⊥ EF . Therefore DA is ...
... Solution. Suppose without loss of generality that AB > AC. If M is the midpoint of BC, since BG : GC = AB : AC, BG > GC so that G lies between M and C and A lies between E and F . Let P be the intersection of DF and EG. Observe that D is the midpoint of the arc BC and that AD ⊥ EF . Therefore DA is ...
Numeration 2016 - Katedra matematiky
... (i) For every α ∈ Cγ there exists some n ∈ N0 with α + n ∈ F0 (γ) ∪ F1 (γ). (ii) F1 (γ) consists of fundamental CNS bases for Z[γ]. Here the algebraic integer β is called a fundamental CNS basis for O if it satisfies the following properties: (1) β − n is a CNS basis for O for all n ∈ N0 . (2) β + 1 ...
... (i) For every α ∈ Cγ there exists some n ∈ N0 with α + n ∈ F0 (γ) ∪ F1 (γ). (ii) F1 (γ) consists of fundamental CNS bases for Z[γ]. Here the algebraic integer β is called a fundamental CNS basis for O if it satisfies the following properties: (1) β − n is a CNS basis for O for all n ∈ N0 . (2) β + 1 ...
Primal Scream - University of Oklahoma
... In the original problem, Pierre is given P , and states that it is not primal. Serge states that his number S is good. Since Pierre is then able to determine the factorization of P , it must be that P is distinguishable. Since Serge can then deduce the numbers, S must distinguish only P . The wordin ...
... In the original problem, Pierre is given P , and states that it is not primal. Serge states that his number S is good. Since Pierre is then able to determine the factorization of P , it must be that P is distinguishable. Since Serge can then deduce the numbers, S must distinguish only P . The wordin ...
sequences and series
... So there are 14 terms in the sequence. Example 3 : At which term does the sequence 36, 43, 50, 57, ... first exceed 1000? un 7n 29 7n 29 1000 7n 971 n 138.714... n 139 The sequence first exceeds 1000 at the 139 term, which is (7 × 139) + 29 = 1002. ...
... So there are 14 terms in the sequence. Example 3 : At which term does the sequence 36, 43, 50, 57, ... first exceed 1000? un 7n 29 7n 29 1000 7n 971 n 138.714... n 139 The sequence first exceeds 1000 at the 139 term, which is (7 × 139) + 29 = 1002. ...
