… We encode the binomials belonging to the toric ideal I A associated with an integral d×n
matrix A using a short sum of rational functions as introduced by Barvinok (Math. Operations …

… For brevity, we also call it a short rational function for the generating function f(P, z). For
example, suppose we have the polytope in Figure 1.1. Then we can write: f(P, z) = z1 5 +z1 4z2 +…

… these applications (including the ones not done in this paper) through three key examples
… In order to illustrate how this works, we shall first offer a brief review of the relevant AJ maps. …

… functions. These results have analogous applications to the study of toric K-stability of toric …
In order to keep our notation short, we shall denote by \(\mathrm{d}\sigma \) the measure on \(\…

… The facts that the graded algebra grvR be Noetherian and that its Poincaré series be a
rational function are not equivalent. The following example in dimension 3 due to Cossart, …

… ], we applied ideas from toric dynamical systems and toric geometry to obtain … function, a m
× p matrix G(s) of rational functions, and s ↦→ row space[I : G(s)] is the corresponding rational …

… These notes cover a short course on symplectic toric manifolds, delivered in six lectures at …
Algebraic geometers and combinatorialists have found fruitful applications of toric varieties to …

… , a function defined near a point P means a rational function regular at P, an element of OV,P
. Since linear forms vanish at the origin, we require our rational functions to … After this short …

… character devoted to a brief introduction in toric geometry with focus on … applications of the
constructed kernels, for instance, to produce a class of residue currents associated with toric …

… the rational functions defining f. We also approach the implicitization problem considering the
toric … Both representations have a wide range of applications in Computer Aided Geometric …