  Consider k x n matrices with rank conditions placed on intervals of columns.
The ranks that are actually achievable correspond naturally to upper triangular
partial permutation matrices, and we call the corresponding subvarieties of
Gr(k,n) the _interval positroid varieties_, as this class lies within the class
of positroid varieties studied in [Knutson-Lam-Speyer]. It includes Schubert
and opposite Schubert varieties, and their intersections, and is Grassmann dual
to the projection varieties of [Billey-Coskun].
  Vakil's "geometric Littlewood-Richardson rule" [Vakil] uses certain
degenerations to positively compute the H^*-classes of Richardson varieties,
each summand recorded as a (2+1)-dimensional "checker game". We use his same
degenerations to positively compute the K_T-classes of interval positroid
varieties, each summand recorded more succinctly as a 2-dimensional "K-IP pipe
dream". In Vakil's restricted situation these IP pipe dreams biject very simply
to the puzzles of [Knutson-Tao].
  We relate Vakil's degenerations to Erd\H os-Ko-Rado shifting, and include
results about computing "geometric shifts" of general T-invariant subvarieties
of Grassmannians.
