We introduce the concept of Schubert graphs, as Schubert spaces---in the meaning of A. Bichara and C. Somma [Rend. Mat. (7) 6 (1986), no. 1-2, 59--75 (1988)] —whose lines have exactly two points. They turn out to be isomorphic to particular Cayley graphs of symmetric groups; this leads also to a new proof of a well-known characterization of symmetric groups. In connection with Bichara and Somma's work [op. cit.], we prove that a Schubert graph is isomorphic to the graph representing the flags of a Boolean lattice. Finally, we discuss the independence of the axioms.
Schubert Graphs, Symmetric Groups and Flags of Boolean Lattices
BURATTI, Marco
1993
Abstract
We introduce the concept of Schubert graphs, as Schubert spaces---in the meaning of A. Bichara and C. Somma [Rend. Mat. (7) 6 (1986), no. 1-2, 59--75 (1988)] —whose lines have exactly two points. They turn out to be isomorphic to particular Cayley graphs of symmetric groups; this leads also to a new proof of a well-known characterization of symmetric groups. In connection with Bichara and Somma's work [op. cit.], we prove that a Schubert graph is isomorphic to the graph representing the flags of a Boolean lattice. Finally, we discuss the independence of the axioms.File in questo prodotto:
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