Geodesic
Some properties of coefficients of the Kolchin dimension polynomial
Fundamentalʹnaâ i prikladnaâ matematika, Tome 24 (2022) no. 1, pp. 165-176 
M. V. Kondratieva. Some properties of coefficients of the Kolchin dimension polynomial. Fundamentalʹnaâ i prikladnaâ matematika, Tome 24 (2022) no. 1, pp. 165-176. http://geodesic.mathdoc.fr/item/FPM_2022_24_1_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

This paper presents a formula expressing Macaulay constants of a numerical polynomial through its minimizing coefficients. From this, we obtain that Macaulay constants of Kolchin dimension polynomials do not decrease. For the minimal differential dimension polynomial $\omega_{\mathcal G/\mathcal F}$ (this concept was introduced by W. Sitt) we will prove a criterion for Macaulay constants to be equal. In this case, as our example shows, there are no bounds from above to the Macaulay constants of the polynomial $\omega_{\xi/\mathcal F}$ for $\mathcal G=\mathcal F\langle\xi\rangle$.

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