Youngmee Koh

On k-hypertournament matrices

Abstract A k -hypertournament is a complete k -hypergraph with all k -edges endowed with orientations. The incidence matrix associated with a k -hypertournament is called a k -hypertournament matrix. Some properties of the hypertournament matrices are investigated. The sequences of the numbers of 1’s and −1’s of rows of a k -hypertournament matrix are respectively called the score sequence and the losing score sequence of the matrix and so of the corresponding hypertournament. A necessary and sufficient condition for a sequence to be the score (and losing score) sequence of a k -hypertournament is considered. We also find some conditions for the existence of k -hypertournament matrices with constant score sequence, called regular k -hypertournament matrices.

DIVISORS OF THE PRODUCTS OF CONSECUTIVE INTEGERS

In this Paper, We look at 3 Simple function L assigning to an integer n the smallest positive integer n such that any product of n consecutive numbers is divisible by n. Investigated are the interesting properties of the function. The function L(n) is completely determined by L(pk/), where pk/ is a factor of n, and satisfies L(mn) L(m)+L(n), where the equality holds for infinitely many cases.