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math.AC2017
Combinatorics of involutive divisions
Michela Ceria
The classical involutive division theory by Janet decomposes in the same way both the ideal and the escalier. The aim of this paper, following Janet's approach, is to discuss the c…
math.RA2017
Buchberger-Zacharias Theory of Multivariate Ore Extensions
Michela Ceria
We present Buchberger Theory and Algorithm of Gröbner bases for multivariate Ore extensions of rings presented as modules over a principal ideal domain. The algorithms are based on…
math.CO2017
Bar code for monomial ideals
Michela Ceria
Aim of this paper is to count -dimensional stable and strongly stable ideals in and variables, given their (constant) affine Hilbert polynomial. To do so, we define the…