منابع مشابه
On Vector Partition Functions
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 expli...
متن کاملOn vector partition functions with negative weights
We introduce the notion of weights into the vector partition function and the volume function associated to a sequence of vectors. We prove an explicit formula for the volume function with possibly negative weights. It is a generalization of a formula given by Brion and Vergne in [2].
متن کاملVector Partition Functions and Generalized Dahmen-micchelli Spaces
This is the first of a series of papers on partition functions and the index theory of transversally elliptic operators. In this paper we only discuss algebraic and combinatorial issues related to partition functions. The applications to index theory will appear in [4]. Here we introduce a space of functions on a lattice which generalizes the space of quasi–polynomials satisfying the difference...
متن کاملAn Explicit Formulation for Two Dimensional Vector Partition Functions
In this paper, an explicit formulation for two dimensional multivariate truncated power functions is presented, and a simplified explicit formulation for two dimensional vector partition functions is given. Moreover, Popoviciu’s formulation for restricted integer partition functions is generalized and the generalized Frobenius problem is also discussed.
متن کاملThe Vector Partition Problem for Convex Objective Functions
The partition problem concerns the partitioning of a given set of n vectors in d-space into p parts to maximize an objective function that is convex on the sum of vectors in each part. The problem has broad expressive power and captures NP-hard problems even if either p or d is fixed. In this article we show that when both p d are fixed, the problem is solvable in strongly polynomial time using...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1995
ISSN: 0097-3165
DOI: 10.1016/0097-3165(95)90067-5