On Vector Partition Functions
نویسنده
چکیده
Vector part i t ion functions appear in m a n y areas of mathemat ics and its applications, including representat ion theory [ 9 ] , commuta t ive algebra [ 14], approximat ion theory [ 4 ] and statistics [5 ] . It was shown by Blakley [ 2 ] that there exists a finite decomposi t ion of N d such that ~b A is a polynomial of degree n d on each piece. Here we describe such a decomposi t ion explicitly and we analyze how the polynomials differ f rom piece to piece. Our construct ion uses the geometric decomposi t ion into chambers studied by Alekseevskaya, Gel ' land and Zelevinsky in [ 1 ]. Within each chamber we give a formula which refines
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