Combinatorial differential algebra of xp. (January 2023)

• Record Type: Journal Article
• Authors: Ait El Manssour, Rida; Sattelberger, Anna-Laura
• Is Part Of: Journal of symbolic computation. Volume 114(2023)
• Page Start: 193
• Page End: 208
• Publication Date: 2023-01
• Subjects: primary 05E40 13P10 12H05 -- secondary 52B20; Differential ideal -- Gröbner basis -- Multivariate jet -- Perfect graph -- Regular triangulation -- Ehrhart polynomial; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2022.04.010
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We link n -jets of the affine monomial scheme defined by x p to the stable set polytope of some perfect graph. We prove that, as p varies, the dimension of the coordinate ring of a certain subscheme of the scheme of n -jets as a C -vector space is a polynomial of degree n + 1, namely the Ehrhart 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 p . We generalize Zobnin's result to the bivariate case. We study ( m, n ) -jets, a higher-dimensional analog of jets, and relate them to regular unimodular triangulations.