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
matteo@alum.mit.edu

Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012, USA
yanhuaf@math1.cims.nyu.edu

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


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