  Bipartite determinantal ideals are introduced by Illian and the author as a
vast generalization of the classical determinantal ideals intensively studied
in commutative algebra, algebraic geometry, representation theory and
combinatorics. We introduce a combinatorial model called concurrent vertex maps
to describe the Stanley-Reisner complex of the initial ideal of any bipartite
determinantal ideal, and study properties and applications of this model
including vertex decomposability, shelling orders, formulas of the Hilbert
series and $h$-polynomials.
