We prove an identity in the double algebra of a Peano space, using techniques first developed by Doubilet, Rota, and Stein, which yields a class of geometric identities in \(n\)-dimensional projective space. Special cases of this identity include a theorem of Bricard in the projective plane and one
Geometric Identities in Lattice Theory
โ Scribed by Matteo Mainetti; Catherine Huafei Yan
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 385 KB
- Volume
- 91
- Category
- Article
- ISSN
- 0097-3165
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๐ SIMILAR VOLUMES
A class of identities in the Grassmann Cayley algebra which yields a large number of geometric theorems on the incidence of subspaces of projective spaces was found by Hawrylycz (``Geometric Identities in Invariant Theory,'' Ph.D. thesis, Massachusetts, Institute of Technology, 1994). In this paper
Our main discovery is the following identity: non-empty subsets of D = [ I, 2. . 11) AHLSWEDE AND ZHANG THEOREM 1. For ever)! ,fbmil>~ .d qf' non-rrnpt?) suh.yet,s nf'Q = ( 1, 2, . . . . tl i i w+ ,=I i 0 i Proof: Note first that only the minimal elements in .d determine X,,, and therefore matter. W