Academic Bibliography

 Search 200 years of publications by Ghent University researchers.
Advanced search
2 files | 992.91 KB
Add to list
  1. Search results
  2. Polarization and depolarization of mo...

Polarization and depolarization of monomial ideals with application to multi-state system reliability

Fatemeh Mohammadi (UGent) , Patricia Pascual-Ortigosa, Eduardo Sáenz-de-Cabezón and Henry P. Wynn
(2020) JOURNAL OF ALGEBRAIC COMBINATORICS. 51(4). p.617-639
Author
Organization
Abstract
Polarization is a powerful technique in algebra which provides combinatorial tools to study algebraic invariants of monomial ideals. We study the reverse of this process, depolarization which leads to a family of ideals which share many common features with the original ideal. Given a squarefree monomial ideal, we describe a combinatorial method to obtain all its depolarizations, and we highlight their similar properties such as the graded Betti numbers. We show that even though they have many similar properties, their differences in dimension make them distinguishable in applications in system reliability theory. In particular, we apply polarization and depolarization tools to study the reliability of multistate coherent systems via binary systems and vice versa. We use depolarization as a tool to reduce the dimension and the number of variables in coherent systems.
Keywords
Monomial ideals, Polarization, Depolarization, Algebraic reliability, OUT-OF-N, PROJECTIVE DIMENSION, REGULARITY, RESOLUTIONS, DIVISORS, MODULES, GRAPHS, BOUNDS, DEPTH

Downloads

  • Download
    Polarization.pdf
    • full text (Accepted manuscript)
    • |
    • open access
    • |
    • PDF
    • |
    • 456.30 KB
  • Download
    (...).pdf
    • full text (Published version)
    • |
    • UGent only
    • |
    • PDF
    • |
    • 536.61 KB

Citation

Please use this url to cite or link to this publication:

MLA
Mohammadi, Fatemeh, et al. “Polarization and Depolarization of Monomial Ideals with Application to Multi-State System Reliability.” JOURNAL OF ALGEBRAIC COMBINATORICS, vol. 51, no. 4, 2020, pp. 617–39, doi:10.1007/s10801-019-00887-6.
APA
Mohammadi, F., Pascual-Ortigosa, P., Sáenz-de-Cabezón, E., & Wynn, H. P. (2020). Polarization and depolarization of monomial ideals with application to multi-state system reliability. JOURNAL OF ALGEBRAIC COMBINATORICS, 51(4), 617–639. https://doi.org/10.1007/s10801-019-00887-6
Chicago author-date
Mohammadi, Fatemeh, Patricia Pascual-Ortigosa, Eduardo Sáenz-de-Cabezón, and Henry P. Wynn. 2020. “Polarization and Depolarization of Monomial Ideals with Application to Multi-State System Reliability.” JOURNAL OF ALGEBRAIC COMBINATORICS 51 (4): 617–39. https://doi.org/10.1007/s10801-019-00887-6.
Chicago author-date (all authors)
Mohammadi, Fatemeh, Patricia Pascual-Ortigosa, Eduardo Sáenz-de-Cabezón, and Henry P. Wynn. 2020. “Polarization and Depolarization of Monomial Ideals with Application to Multi-State System Reliability.” JOURNAL OF ALGEBRAIC COMBINATORICS 51 (4): 617–639. doi:10.1007/s10801-019-00887-6.
Vancouver
1.
Mohammadi F, Pascual-Ortigosa P, Sáenz-de-Cabezón E, Wynn HP. Polarization and depolarization of monomial ideals with application to multi-state system reliability. JOURNAL OF ALGEBRAIC COMBINATORICS. 2020;51(4):617–39.
IEEE
[1]
F. Mohammadi, P. Pascual-Ortigosa, E. Sáenz-de-Cabezón, and H. P. Wynn, “Polarization and depolarization of monomial ideals with application to multi-state system reliability,” JOURNAL OF ALGEBRAIC COMBINATORICS, vol. 51, no. 4, pp. 617–639, 2020.
@article{8667441,
  abstract     = {{Polarization is a powerful technique in algebra which provides combinatorial tools to study algebraic invariants of monomial ideals. We study the reverse of this process, depolarization which leads to a family of ideals which share many common features with the original ideal. Given a squarefree monomial ideal, we describe a combinatorial method to obtain all its depolarizations, and we highlight their similar properties such as the graded Betti numbers. We show that even though they have many similar properties, their differences in dimension make them distinguishable in applications in system reliability theory. In particular, we apply polarization and depolarization tools to study the reliability of multistate coherent systems via binary systems and vice versa. We use depolarization as a tool to reduce the dimension and the number of variables in coherent systems.}},
  author       = {{Mohammadi, Fatemeh and Pascual-Ortigosa, Patricia and Sáenz-de-Cabezón, Eduardo and Wynn, Henry P.}},
  issn         = {{0925-9899}},
  journal      = {{JOURNAL OF ALGEBRAIC COMBINATORICS}},
  keywords     = {{Monomial ideals,Polarization,Depolarization,Algebraic reliability,OUT-OF-N,PROJECTIVE DIMENSION,REGULARITY,RESOLUTIONS,DIVISORS,MODULES,GRAPHS,BOUNDS,DEPTH}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{617--639}},
  title        = {{Polarization and depolarization of monomial ideals with application to multi-state system reliability}},
  url          = {{http://doi.org/10.1007/s10801-019-00887-6}},
  volume       = {{51}},
  year         = {{2020}},
}
Altmetric
View in Altmetric
Web of Science
Times cited: