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http://hdl.handle.net/2445/129787
Title: | On the minimality of GT-systems |
Author: | Salat Moltó, Martí |
Director/Tutor: | Miró-Roig, Rosa M. (Rosa Maria) |
Keywords: | Matrius (Matemàtica) Anells artinians Treballs de fi de màster Varietats algebraiques Geometria diferencial Geometria projectiva Àlgebra commutativa Matrices Artin rings Master's theses Algebraic varieties Differential geometry Projective geometry Commutative algebra |
Issue Date: | 27-Jun-2018 |
Abstract: | [en] In this work we address the minimality problem of GT-systems in three variables introduced in [8]. To study this problem, we consider an $N \times N$ generic sparse circulant matrix $M$ with only three non-zero entries per row: $x_0, x_a$ and $x_b$ . We consider $d _{(N;0,a,b)}$ (resp. $p_{( N;0,a,b)}$) the number of non-zero coefficients in the expansion of the determinant (resp. the permanent) of $M$. The minimality of a GT-system is translated to the equality between $d_{(N;0,a,b)}$ and $p_{(N;0,a,b)}$ with gcd $(a,b,N)=1$. We prove that this equality holds in some open cases giving rise to new minimality results. |
Note: | Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2018, Director: Rosa Maria Miró-Roig |
URI: | http://hdl.handle.net/2445/129787 |
Appears in Collections: | Màster Oficial - Matemàtica Avançada |
Files in This Item:
File | Description | Size | Format | |
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memoria.pdf | Memòria | 229.29 kB | Adobe PDF | View/Open |
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