On the coefficients of the permanent and the determinant of a circulant matrix: Applications
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- by Liena Colarte, Emilia Mezzetti, Rosa M. Miró-Roig and Martí Salat PDF
- Proc. Amer. Math. Soc. 147 (2019), 547-558 Request permission
Abstract:
Let $d(N)$ (resp., $p(N)$) be the number of summands in the determinant (resp., permanent) of an $N\times N$ circulant matrix $A=(a_{ij})$ given by $a_{ij}=X_{i+j}$ where $i+j$ should be considered mod $N$. This short note is devoted to proving that $d(N)=p(N)$ if and only if $N$ is a prime power. We then give an application to homogeneous monomial ideals failing the Weak Lefschetz property.References
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Additional Information
- Liena Colarte
- Affiliation: Department de matemàtiques i Informàtica, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain
- Email: liena.colarte@ub.edu
- Emilia Mezzetti
- Affiliation: Dipartimento di Matematica e Geoscienze, Università di Trieste, Via Valerio 12/1, 34127 Trieste, Italy
- MR Author ID: 209573
- ORCID: 0000-0001-5300-9779
- Email: mezzette@units.it
- Rosa M. Miró-Roig
- Affiliation: Department de matemàtiques i Informàtica, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain
- MR Author ID: 125375
- ORCID: 0000-0003-1375-6547
- Email: miro@ub.edu
- Martí Salat
- Affiliation: Department de matemàtiques i Informàtica, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain
- Email: msalatmo7@alumnes.ub.edu
- Received by editor(s): February 11, 2018
- Received by editor(s) in revised form: May 28, 2018
- Published electronically: November 5, 2018
- Additional Notes: The second author was a member of INdAM - GNSAGA and was supported by PRIN “Geometry of algebraic varieties”.
The third author was partially supported by MTM2016–78623-P - Communicated by: Claudia Polini
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 547-558
- MSC (2010): Primary 15B05, 15A15, 13E10
- DOI: https://doi.org/10.1090/proc/14296
- MathSciNet review: 3894894