35 research outputs found
Ideals of Adjacent Minors
We give a description of the minimal primes of the ideal generated by the 2 x
2 adjacent minors of a generic matrix. We also compute the complete prime
decomposition of the ideal of adjacent m x m minors of an m x n generic matrix
when the characteristic of the ground field is zero. A key intermediate result
is the proof that the ideals which appear as minimal primes are, in fact, prime
ideals. This introduces a large new class of mixed determinantal ideals that
are prime
A finiteness theorem for Markov bases of hierarchical models
We show that the complexity of the Markov bases of multidimensional tables
stabilizes eventually if a single table dimension is allowed to vary. In
particular, if this table dimension is beyond a computable bound, the Markov
bases consist of elements of Markov bases of smaller tables. We give an
explicit formula for this bound in terms of Graver bases. We also compute these
Markov and Graver complexities for all tables.Comment: 13 pages, 1 figur
Normal Toric Ideals of Low Codimension
Every normal toric ideal of codimension two is minimally generated by a
Grobner basis with squarefree initial monomials. A polynomial time algorithm is
presented for checking whether a toric ideal of fixed codimension is normal