8 citations · 8 across the 6 of their papers we have counts for
9 papers
Relation morphisms of directed graphs
Gilles G. de Castro, Francesco D'Andrea, Piotr M. Hajac
Associating graph algebras to directed graphs leads to both covariant and contravariant functors from suitable categories of graphs to the category k-Alg of algebras and algebra ho…
The maximal dimensions of path and graph algebras
Piotr M. Hajac, Elizabeth A. Pacheco, Åukasz Kaczmarczyk +1
We consider the class of acyclic connected directed graphs with . In this paper we find the optimal upper bound for the number of paths amongst acyclic, connected graphs w…
The functoriality of moves on graphs and the extended covariant functoriality of graph algebras
Gilles G. de Castro, Piotr M. Hajac, Mateusz Lowiel +1
Combinatorics of graphs is a very powerful tool to unravel various properties of graph algebras. In particular, isomorphisms between graph algebras are often implemented by moves b…
Milnor meets Hopf and Toeplitz at the K-theory of quantum projective planes
Francesco D'Andrea, Piotr M. Hajac, Tomasz Maszczyk +1
We explore applications of the celebrated construction of the Milnor connecting homomorphism from the odd to the even K-groups in the context of Hopf--Galois theory. For a finitely…
Rank-two Milnor idempotents for the multipullback quantum complex projective plane
Carla Farsi, Piotr M. Hajac, Tomasz Maszczyk +1
The -group of the C*-algebra of multipullback quantum complex projective plane is known to be , with one generator given by the C*-algebra itself, one given by t…
Counting paths in directed graphs
Piotr M. Hajac, Oskar M. Stachowiak
We consider the class of directed graphs with edges and without loops shorter than . Using the concept of a labelled graph, we determine graphs from this class th…