  We determine a Groebner basis for the secant ideal of the toric ideal
associated to the second hypersimplex, with respect to any circular term order.
The Groebner basis of the secant ideal requires polynomials of odd degree up to
n. This shows that the circular term order is 2-delightful, resolving a
conjecture of Drton, Sturmfels, and the author. The proof uses Groebner
degenerations for secant ideals, combinatorial characterizations of the secant
ideals of monomial ideals, and the relations between secant ideals and
prolongations.
