Annals of Combinatorics 2 (1998) 243-289

Graphical 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

Get the LaTex | DVI | PS file of this abstract.