... = uv and e = u v are said to be noncrossing if u = u , v = v , and u and u are in the same order as v and v ; in other words, if u u and v v or u u and v v A matching of G is called planar if ... tableaux of the same shape and with a “descendtype” property (Theorem 10) Our arguments can be adapted in order to characterize the distribution of the largest size of planar subgraphs of randomly ... row inserting π(1), , π(m) to an initially empty pair of tableaux, and thus obtaining P(π), and, • placing the value i into the box of Q(π)’s diagram corresponding to the box created during the...