Species Over a Finite Field
Anthony Henderson
School of Mathematics and Statistics University of Sydney NSW 2006 Australia
DOI: 10.1007/s10801-005-6905-1
Abstract
We generalize Joyal 
s theory of species to the case of functors from the groupoid of finite sets to the category of varieties over F q. These have cycle index series defined by counting fixed points of twisted Frobenius maps. We give an application to configuration spaces.
s theory of species to the case of functors from the groupoid of finite sets to the category of varieties over F q. These have cycle index series defined by counting fixed points of twisted Frobenius maps. We give an application to configuration spaces.Pages: 147–161
Keywords: keywords species; finite field; configuration space
Full Text: PDF
References
1. F. Bergeron, G. Labelle, and P. Leroux, Combinatorial Species and Tree-like Structures, vol. 67 of Encyclopedia of Mathematics and its Applications, Cambridge University Press, 1998.
2. W. Fulton and R. Macpherson, “A compactification of configuration spaces,” Ann. of Math. 139 (1994), 183- 225.
3. E. Getzler, “Mixed Hodge structures of configuration spaces,” preprint, MPI-96-61, http://arxiv.org/abs/alggeom/9510018.
4. A. Joyal, “Une théorie combinatoire des séries formelles,” Adv. Math. 42 (1981), 1-82.
5. A. Joyal, “Foncteurs analytiques et esp`eces de structures,” in Combinatoire Énumérative (Quebec, 1985), vol. 1234 of Lecture Notes in Mathematics, Springer, Berlin, 1986, pp. 126-159.
6. M. Kisin and G.I. Lehrer, “Equivariant Poincaré polynomials and counting points over finite fields,” J. Algebra 247 (2002), 435-451.
7. I.G. Macdonald, Symmetric Functions and Hall Polynomials, 2nd ed., Oxford Univ. Press, 1995.
8. Y.I. Manin, “Generating functions in algebraic geometry and sums over trees,” in The Moduli space of Curves (Texel Island, 1994), vol. 129 of Progress in Mathematics, Birkhauser Boston, Boston, 1995, pp. 401-417.
9. Y.I. Manin, Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces, vol. 47 of American Mathematical Society Colloquium Publications, American Mathematical Society, 1999.
2. W. Fulton and R. Macpherson, “A compactification of configuration spaces,” Ann. of Math. 139 (1994), 183- 225.
3. E. Getzler, “Mixed Hodge structures of configuration spaces,” preprint, MPI-96-61, http://arxiv.org/abs/alggeom/9510018.
4. A. Joyal, “Une théorie combinatoire des séries formelles,” Adv. Math. 42 (1981), 1-82.
5. A. Joyal, “Foncteurs analytiques et esp`eces de structures,” in Combinatoire Énumérative (Quebec, 1985), vol. 1234 of Lecture Notes in Mathematics, Springer, Berlin, 1986, pp. 126-159.
6. M. Kisin and G.I. Lehrer, “Equivariant Poincaré polynomials and counting points over finite fields,” J. Algebra 247 (2002), 435-451.
7. I.G. Macdonald, Symmetric Functions and Hall Polynomials, 2nd ed., Oxford Univ. Press, 1995.
8. Y.I. Manin, “Generating functions in algebraic geometry and sums over trees,” in The Moduli space of Curves (Texel Island, 1994), vol. 129 of Progress in Mathematics, Birkhauser Boston, Boston, 1995, pp. 401-417.
9. Y.I. Manin, Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces, vol. 47 of American Mathematical Society Colloquium Publications, American Mathematical Society, 1999.