# Combinatorial Differential Algebra of xp

@article{Manssour2021CombinatorialDA, title={Combinatorial Differential Algebra of xp}, author={Rida Ait El Manssour and Anna-Laura Sattelberger}, journal={ArXiv}, year={2021}, volume={abs/2102.03182} }

We link n -jets of the affine monomial scheme defined by x to the stable set polytope of some perfect graph. We prove that, as p varies, the dimension of the coordinate ring of the scheme of n -jets as a C -vector space is a polynomial of degree n+1, namely the Erhart polynomial of the stable set polytope of that graph. One main ingredient for our proof is a result of Zobnin who determined a differential Gröbner basis of the differential ideal generated by x. We generalize Zobnin’s result to… Expand

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