2022/02/05 by M. V. Kondratieva, Kondratieva, M. V.
Mathematics · #Mathematical functions and polynomials #Analytic and geometric function theory #Commutative Algebra and Its Applications
paper · pdf · doi:10.48550/arxiv.2202.02542
The article presents a formula expressing Macaulay constants of a numerical polynomial through its minimizing coefficients. From this, we have that Macaulay constants of Kolchin dimension polynomials do not decrease. For the minimal differential dimension polynomial (this concept was introduced by W.Sitt in [5]) we will prove a criterion for Macaulay constants to be equal. In this case, as the example (2) shows, there are no bounds from above to the Macaulay constants of the dimension polynomial for starting generator.