A homogeneous ideal is robust if its universal Gr ?obner basis is also a minimal generating set. For toric ideals, one has the stronger... Show moreA homogeneous ideal is robust if its universal Gr ?obner basis is also a minimal generating set. For toric ideals, one has the stronger definition: A toric ideal is strongly robust if its Graver basis equals the set of indispensable binomials. We characterize the codimension 2 strongly robust toric ideals by their Gale diagrams. This gives a positive answer to a question of Petrovi?, Thoma, and Vladoiu in the case of codimension 2 toric ideals. Show less
The strand symmetric model is a phylogenetic model designed to reflect the symmetry inherent in the double-stranded structure of DNA. We show... Show moreThe strand symmetric model is a phylogenetic model designed to reflect the symmetry inherent in the double-stranded structure of DNA. We show that the set of known phylogenetic invariants for the general strand symmetric model of the three leaf claw tree entirely defines the ideal. This knowledge allows one to determine the vanishing ideal of the general strand symmetric model of any trivalent tree. Our proof of the main result is computational. We use the fact that the Zariski closure of the strand symmetric model is the secant variety of a toric variety to compute the dimension of the variety. We then show that the known equations generate a prime ideal of the correct dimension using elimination theory. Show less
