Corpus ID: 231839614

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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