3 papers
math.CO2026
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…
math.OA2026
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…
math.RA2024
Williams' and Graded Equivalence Conjectures for small graphs
Roozbeh Hazrat, Elizabeth Pacheco
We prove what might have been expected: The Williams Conjecture in symbolic dynamics and Graded Morita Equivalence Conjecture for Leavitt/-graph algebras hold for ``small grap…