Floor decomposition of tropical planar curves

Abstract

Mikhalkin showed that when counted with appropriate (r-real) multiplicities, the number of tropical curves in (R*)2 of genus g and Newton polygon Δ passing through s generic points in (R*)2 agrees with the corresponding Gromov-Witten (resp. Welschinger) invariants. Brugalle and Mikhalkin show that the enumeration of these tropical curves can be reduced to the enumeration of certain combinatorial objects called floor diagrams. We study these floor diagrams and their applications.