Miró-Roig, Rosa M. (Rosa Maria)Salat Moltó, Martí2019-03-062019-03-062018-06-27https://hdl.handle.net/2445/129787Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2018, Director: Rosa Maria Miró-Roig[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.30 p.application/pdfengcc-by-sa (c) Martí Salat Moltó, 2018http://creativecommons.org/licenses/by-nc-sa/3.0/es/Matrius (Matemàtica)Anells artiniansTreballs de fi de màsterVarietats algebraiquesGeometria diferencialGeometria projectivaÀlgebra commutativaMatricesArtin ringsMaster's thesesAlgebraic varietiesDifferential geometryProjective geometryCommutative algebrainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/openAccess