BETTI TABLES OF MONOMIAL IDEALS FIXED BY PERMUTATIONS OF THE VARIABLES

摘要

Let S-n be a polynomial ring with n variables over a field and {I-n}(n >= 1) a chain of ideals such that each I-n is a monomial ideal of S-n fixed by permutations of the variables. In this paper, we present a way to determine all nonzero positions of Betti tables of I-n for all large intergers n from the Z(m)-graded Betti tables of I-m for some small integers m. Our main result shows that the projective dimension and the regularity of I-n eventually become linear functions on n, confirming a special case of conjectures posed by Le, Nagel, Nguyen and Romer.