No abstract

In this paper we show how to embed A∗, the dual of the mod 2 Steenrod\ud algebra, into a certain inverse limit of algebras of invariants of the general linear group.\ud The prime 2 is fixed throughout the pape

A well-known fact in Spectral Graph Theory is the existence of pairs of isospectral nonisomorphic graphs (known as PINGS). The work of A.J. Schwenk (in 1973) and of C. Godsil and B. McKay (in 1982) shed some light on the explanation of the presence of isospectral graphs, and they gave routines to construct PINGS. Here, we consider the Godsil-McKay-type routines developed for graphs, whose adjacency matrices are (0, 1)-matrices, to the level of signed graphs, whose adjacency matrices allow the presence of −1's. We show that, with suitable adaption, such routines can be successfully ported to signed graphs, and we can built pairs of cospectral switching nonisomorphic signed graphs. (2010): 05C22, 05C50 Mathematics Subject Classification

No abstract

In 2005, William M. Singer introduced the notion of k-algebra with\ud coproducts for any commutative ring k, and showed that the algebra of operations\ud on the cohomology ring of any cocommutative F2-Hopf algebra can be endowed\ud with such structure. In this paper we show that the same is true when the ground\ud field of the cocommutative Hopf algebra is Fp, p is any odd prime, and the algebra\ud of operations B(p) is equipped with an exotic coproduct. We also give an explicit\ud description of the coalgebra with products dual to B(p)