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. - In: JOURNAL OF GEOMETRY. - ISSN 0047-2468. - 48:(1993), pp. 10-22.
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
