2) Complete the following statement (correctly) : Let and n be positive integers. Then there is...
Question:
2) Complete the following statement (correctly) :
Let λ and n be positive integers. Then there is a λ-fold TS(n) if and only if .
3) There is only one idempotent quasigroup of order 3 on symbols {1, 2, 3}; find its table, a LS(3).
If it is used in the 3n + 1 construction of a 2-fold TS(10), find the two triples containing each of the following pairs:
a) (2, 1), (3, 3)
b) (3, 1), (3, 3)
c) ∞ , (2, 2)
4) Wilson's Construction is to be used to construct a STS(13). Find the appropriate deficiency graph, and a 1-factorization of it.
5) Here is a solution to Heffter's difference problem for a cyclic STS(13) on the integers (mod 13): the two difference triples are {1, 3, 4} and {2, 5, 6}.
a) Find the two corresponding base blocks.
b) Find the third element in the triple containing each of the following pairs:
i) 2, 12 ii) 0, 3 iii) 5, 7
Bonus Problem: (10 extra points)
Let V be a finite, non-empty set. Prove that there is a PBD on V with every block having size 2.
Probability and Statistics
ISBN: 978-0321500465
4th edition
Authors: Morris H. DeGroot, Mark J. Schervish