Annals of Combinatorics 2 (1998) 243-289Graphical Operations on Projective Spaces Matteo Mainetti and Catherine Huafei Yan Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012, USA Received May 16, 1998 AMS Subject Classification: 13A50, 05A40, 15A72, 50D20 Abstract. Motivated by the work of Crapo and Rota [6] on the lifting of a projective complex, we introduce a class of invariant operations associated to integral-weighted graphs, which we call graphical operations. Such operations generalize the sixth harmonic of a quadranguler set on a projective line. We determine the expansion of the graphical operations in terms of multi-linear bracket polynomials in a Grassmann-Cayley algebra. Reducibility and compositions of such invariant operations are also investigated with a number of examples. Keywords: invariant operation, projective geometry, Grassmann-Cayley algebra, bracket polynomial |