The main purpose of this book is to introduce algebraic, combinatorial, and computational
methods to study monomial algebras and their presentation ideals, including Stanley …

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In this paper, we recall the object sectional matrix which encodes the Hilbert functions of
successive hyperplane sections of a homogeneous ideal. We translate and/or reprove …

We give a notion of “combinatorial proximity” among strongly stable ideals in a given
polynomial ring with a fixed Hilbert polynomial. We show that this notion guarantees …

The CoCoA project dates back to 1987, with the first public release of its interactive system
in 1989. The aim has always been to provide a userfriendly software laboratory for studying …

We study a poset ℜ on the free monoid (X*) on a countable alphabet X. This poset is
determined by the fact that its total extensions are precisely the standard term orders on X …

We study two partial orders on $[x_1,..., x_n] $, the free abelian monoid on ${x_1,..., x_n} $.
These partial orders, which we call the``strongly stable''and the``stable''partial order, are …

This thesis presents the design of CoCoA, a specialpurpose computer algebra system
dedicated to the Commutative Algebra. After an Introduction to the field of the Computer …

We study the power series ring R= K [[x1, x2, x3,...]] on countably infinitely many variables,
over a field K, and two particular K-subalgebras of it: the ring R, which is isomorphic to an …

We describe two new characterizations of freeness for hyperplane arrangements via the
study of the generic initial ideal and of the sectional matrix of the Jacobian ideal of …