A formula for the total permutation-equivariant K-theoretic   Gromov-Witten potential
  We give a summation over graphs type formula for the permutation-equivariant K-theoretic Gromov-Witten total potential of a projective manifold X in terms of cohomological Gromov-Witten (GW) invariants of X. We achieve this by describing combinatorially the Kawasaki strata of the moduli spaces of stable maps to X. 
Valentin Tonita
math.AG