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Zbl 1186.52006
Boysal, Arzu; Vergne, Michèle
Paradan's wall crossing formula for partition functions and Khovanski-Pukhlikov differential operator. (English)
[J] Ann. Inst. Fourier 59, No. 5, 1715-1752 (2009). ISSN 0373-0956; ISSN 1777-5310/e

Let $A$ be an $r\times N$ integer matrix, denote by $\Phi$ the set of all its column vectors. For any $a\in \mathbb Z^r$ denote the convex polytope $P(\Phi,a):= \{y\in \mathbb R^N_{\ge 0}\mid Ay=a\}$. The function $a \mapsto |P(\Phi,a)\cap \mathbb Z^N|$ is called a partition function. \par It turns out that there is a decomposition of $\mathbb R^r$ in closed chambers such that the partition function is quasi-polynomial in each chamber. P.-E.~Paradan introduced a formula for the jump of the partition function for a couple of neighboring chambers. In the current paper the authors give an algebraic proof of this formula. Furthermore they give a residue formula for the jump which enables to compute it.
[Oleg Karpenkov (Graz)]

MSC 2000:: *52B20 Lattice polytopes (convex geometry)
14M25 Toric varieties, etc.

Keywords: polytopes; toric varieties

Cited in: Zbl 1253.53083

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