Phase transitions from exp?(n1/2) to exp?(n2/3) in the asymptotics of banded plane partitions

We examine the asymptotics of a class banded plane partitions under varying bandwidth parameter m, and clarify transitional behavior for large size n increasing m=m(n) to be from c1n?1exp?(c2n1/2) c3n?49/72exp?(c4n2/3+c5n1/3) some explicit coefficients c1,…,c5. The method proof, which is unified saddle-point analysis all phases, general can extended other classes partitions.