By a plane partition, we mean a finite set, P , of lattice points with positive integer coefficients, {(i, j, k)} ⊆ N, with the property that if (r, s, t) ∈ P and 1 ≤ i ≤ r, 1 ≤ j ≤ s, 1 ≤ k ≤ t, then (i, j, k) must also be in P . A plane partition is symmetric if (i, j, k) ∈ P if and only if (j, i, k) ∈ P . The height of stack (i, j) is the largest value of k for which there exists a point (i,...

In the present work, a single-crystalline epitaxial nonpolar a-plane AlN film with in-plane two-folder symmetries was successfully achieved on an r-plane sapphire substrate, by combining physical vapor deposition and high-temperature annealing technique. Moreover, varying thickness, evolution of crystalline quality structure were systematically investigated using X-ray diffraction, Raman spectr...

We consider two families of plane partitions: totally symmetric self-complementary plane partitions (TSSCPPs) and cyclically symmetric transpose complement plane partitions (CSTCPPs). If T (n) and C(n) are the numbers of such plane partitions in a 2n× 2n× 2n box, then ord2(T (n)) = ord2(C(n)) for all n ≥ 1. We also discuss various consequences, along with other results on ord2(T (n)). 2000 Math...