6 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…
Stable Coherent Systems
Rodrigo Iglesias, Fatemeh Mohammadi, Patricia Pascual-Ortigosa +2
We describe the notion of stability of coherent systems as a framework to deal with redundancy. We define stable coherent systems and show how this notion can help the design of re…
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…
Support posets of some monomial ideals
Patricia Pascual-Ortigosa, Eduardo Sáenz-de-Cabezón
The support poset of a monomial ideal encodes the relation between the variables and the minimal monomial generators of . I…
Algebraic reliability of multi-state -out-of- systems
Patricia Pascual-Ortigosa, Eduardo Sáenz-de-Cabezón, Henry P. Wynn
In this paper we review different definitions that multi-state -out-of- systems have received along the literature and study them in a unified way using the algebra of monomi…
Polarization and depolarization of monomial ideals with application to multistate system reliability
Fatemeh Mohammadi, Patricia Pascual-Ortigosa, Eduardo Sáenz-de-Cabezón +1
We study the family of depolarizations of a squarefree monomial ideal , i.e. all monomial ideals whose polarization is . We describe a method to find all depolarizations of $…