THE DEGENERACY PROBLEM OF TWO-DIMENSIONAL LINEAR RECURRING ARRAYS

The degeneracy degree and degeneracy position sets of a two-dimensional linear recurrence relation set are characterized. The fact that a linear recurring array is essentially a doubly periodic array is shown. By using the Grobner base theory, a calculation formula for degeneracy degree is gived and the existence of a special degeneracy position set is proved. In the present paper, the degeneracy problem of the two-dimensional linear recurring arrays is completely solved.