|
Fundamentalnaya i Prikladnaya Matematika, 2022, Volume 24, Issue 1, Pages 165–176
(Mi fpm1924)
|
|
|
|
Some properties of coefficients of the Kolchin dimension polynomial
M. V. Kondratieva Moscow State University, Department of Mechanics and Mathematics,
Leninskie Gory, Moscow 119992, Russia
Abstract:
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 $\mathcal G=\mathcal F\langle\xi\rangle$.
Citation:
M. V. Kondratieva, “Some properties of coefficients of the Kolchin dimension polynomial”, Fundam. Prikl. Mat., 24:1 (2022), 165–176; J. Math. Sci., 269:5 (2023), 725–733
Linking options:
https://www.mathnet.ru/eng/fpm1924 https://www.mathnet.ru/eng/fpm/v24/i1/p165
|
Statistics & downloads: |
Abstract page: | 101 | Full-text PDF : | 36 | References: | 26 |
|