Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/129787
On the minimality of GT-systems
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[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.
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Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2018, Director: Rosa Maria Miró-Roig
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SALAT MOLTÓ, Martí. On the minimality of GT-systems. [consulted: 6 of June of 2026]. Available at: https://hdl.handle.net/2445/129787