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We present a combinatorial mechanism for counting certain objects associated to a variety over a finite field. The basic example is that of counting conjugacy classes of the general linear group. We discuss how the method applies to counting these and also to counting unipotent matrices and pairs of commuting matrices.[Proceedings of the Primeras Jornadas de Teoría de Números (Vilanova i la Geltrú (Barcelona), 30 June - 2 July 2005)].
@article{Rodríguez2007, abstract = {We present a combinatorial mechanism for counting certain objects associated to a variety over a finite field. The basic example is that of counting conjugacy classes of the general linear group. We discuss how the method applies to counting these and also to counting unipotent matrices and pairs of commuting matrices.[Proceedings of the Primeras Jornadas de Teoría de Números (Vilanova i la Geltrú (Barcelona), 30 June - 2 July 2005)].}, author = {Rodríguez-Villegas, Fernando}, journal = {Publicacions Matemàtiques}, keywords = {Teoría algebraica de números; Función zeta; Campos finitos; Problemas combinatorios; Zeta functions; finite fields; combinatorics}, language = {eng}, number = {Extra}, pages = {209-220}, title = {Counting colorings on varieties.}, url = {http://eudml.org/doc/41922}, volume = {51}, year = {2007}, }
TY - JOUR AU - Rodríguez-Villegas, Fernando TI - Counting colorings on varieties. JO - Publicacions Matemàtiques PY - 2007 VL - 51 IS - Extra SP - 209 EP - 220 AB - We present a combinatorial mechanism for counting certain objects associated to a variety over a finite field. The basic example is that of counting conjugacy classes of the general linear group. We discuss how the method applies to counting these and also to counting unipotent matrices and pairs of commuting matrices.[Proceedings of the Primeras Jornadas de Teoría de Números (Vilanova i la Geltrú (Barcelona), 30 June - 2 July 2005)]. LA - eng KW - Teoría algebraica de números; Función zeta; Campos finitos; Problemas combinatorios; Zeta functions; finite fields; combinatorics UR - http://eudml.org/doc/41922 ER -