W continental ice sheets melted about 15,000 years ago, rising seas inundated large regions of northern Australia, fl ooding valleys and creating vast, low-lying wetland areas. More recent transitions in some of these regions occurred as gradual siltation and levée formation reduced the movement of salt water to create freshwater swamps that were regularly fi lled by monsoon rains, a process th...

Koike, K., On a conjecture of Stanley on Jack symmetric functions, Discrete Mathematics 115 (1993) 211-216. The Jack symmetric function J,(x; G() is a symmetric function with interesting properties that J,(x; 2) is a spherical function of the symmetric pair (GL(n, FQ O(n, [w)) and that J,(x; 1) is the Schur function S,(x). Many interesting conjectures about the combinatorial properties of J,(x;...

We study a novel spline-like basis, which we name the falling factorial basis, bearing many similarities to the classic truncated power basis. The advantage of the falling factorial basis is that it enables rapid, linear-time computations in basis matrix multiplication and basis matrix inversion. The falling factorial functions are not actually splines, but are close enough to splines that they...