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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
References:
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 $\mathcal G=\mathcal F\langle\xi\rangle$.
Funding agency Grant number
Lomonosov Moscow State University
This research has been supported by the Interdisciplinary Scientific and Educational School of Moscow University “Brain, Cognitive Systems, Artificial Intelligence.”
English version:
Journal of Mathematical Sciences (New York), 2023, Volume 269, Issue 5, Pages 725–733
DOI: https://doi.org/10.1007/s10958-023-06309-0
Document Type: Article
UDC: 512.628.2
Language: Russian
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
Citation in format AMSBIB
\Bibitem{Kon22}
\by M.~V.~Kondratieva
\paper Some properties of coefficients of the Kolchin dimension polynomial
\jour Fundam. Prikl. Mat.
\yr 2022
\vol 24
\issue 1
\pages 165--176
\mathnet{http://mi.mathnet.ru/fpm1924}
\transl
\jour J. Math. Sci.
\yr 2023
\vol 269
\issue 5
\pages 725--733
\crossref{https://doi.org/10.1007/s10958-023-06309-0}
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    Фундаментальная и прикладная математика
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