Publications [#47936] of Ruriko Yoshida

Papers Submitted

1. A. Takemura and R. Yoshida, A generalization of the integer linear infeasibility problem, Discrete Optimization (2006) [math.ST/0603108]
   (last updated on 2006/07/01)

   Abstract:
   Does a given system of linear equations with nonnegative constraints have an integer solution? This problem appears in many areas, such as number theory, operations research, and statistics. To study a family of systems with no integer solution, we focus on a commutative semigroup generated by the columns of its defining matrix. In this paper we will study a commutative semigroup generated by a finite subset of $\Z^d$ and its saturation. We show the necessary and sufficient conditions for the given semigroup to have a finite number of elements in the difference between the semigroup and its saturation. Also we define fundamental holes and saturation points of a commutative semigroup. Then, we show the simultaneous finiteness of the difference between the semigroup and its saturation, the set of non-saturation points of the semigroup, and the set of generators for saturation points, which is a set of generator of a monoid. We apply our results to some three and four dimensional contingency tables.