4 papers
Monomial polarization and depolarization of abstract simplicial complexes
Víctor M. López-Antón, Pablo Munarriz-Senosiain, Patricia Pascual-Ortigosa +1
We translate the operations of polarization and depolarization from monomial ideals in a polynomial ring to abstract simplicial complexes. As a result, we explicitly describe the r…
Gröbner bases, resolutions, and the Lefschetz properties for powers of a general linear form in the squarefree algebra
Filip Jonsson Kling, Samuel Lundqvist, Fatemeh Mohammadi +2
For the almost complete intersection ideals , we compute their reduced Gröbner basis for any term ordering, revealing a combinatorial…
On the minimal free resolution of the Rees algebra of tri-generated bivariate monomial ideals
Rodrigo Iglesias, Matthias Orth, Eduardo Sáenz-de-Cabezón +1
Let be a monomial ideal in two variables generated by three monomials and let be its Rees ideal. We describe an algorithm to compute the minimal generating set…
A C++ class for algebraic reliability computations
Anna Maria Bigatti, Patricia Pascual-Ortigosa, Eduardo Sáenz-de-Cabezón
We present the design and implementation of a \texttt{C++} class for reliability analysis of multi-state systems using an algebraic approach based on monomial ideals. The class is…