4 papers
Sharp bounds on the least eigenvalue of a graph determined from edge clique partitions
Domingos M. Cardoso, Inês Serôdio Costa, Rui Duarte
Sharp bounds on the least eigenvalue of an arbitrary graph are presented. Necessary and sufficient (just sufficient) conditions for the lower (upper) bound to be attained are deduc…
Spectral properties of the -Queens' Graphs
Domingos M. Cardoso, Inês Serôdio Costa, Rui Duarte
The -Queens' graph, , is the graph associated to the chessboard (a generalization of the classical chessboard), with vertices, ea…
Pak-Stanley labeling of the -Catalan hyperplane arrangement
Rui Duarte, António Guedes de Oliveira
We characterize in simple terms the Pak-Stanley labels of the regions of the -Catalan arrangement. We also propose a simple algorithm that returns from . Fi…
Partial Parking Functions
Rui Duarte, António Guedes de Oliveira
We characterise the Pak-Stanley labels of the regions of a family of hyperplane arrangements that interpolate between the Shi arrangement and the Ish arrangement.