6 citations · 22 across the 13 of their papers we have counts for
13 papers
The number of Prime Parking Functions
Rui Duarte, António Guedes de Oliveira
A parking function of length is prime if we obtain a parking function of length by deleting one 1 from it. In this note we give a new direct proof that the number of prim…
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.
Between Ish and Shi
Rui Duarte, António Guedes de Oliveira
We introduce a new family of hyperplane arrangements in dimension that includes both the Shi arrangement and the Ish arrangement. We prove that all the members of a given…
The number of parking functions with center of a given length
Rui Duarte, António Guedes de Oliveira
Let and suppose that, when the Depth-first Search Algorithm is applied to a given rooted labelled tree on vertices, exactly vertices are visited before ba…
Note on the bijectivity of the Pak-Stanley labelling
Rui Duarte, António Guedes de Oliveira
This article has the sole purpose of presenting a simple, self-contained and direct proof of the fact that the Pak-Stanley labeling is a bijection. The construction behind the proo…
A short proof of a famous combinatorial identity
Rui Duarte, António Guedes de Oliveira
We explain how the identity is an easy consequence of the inclusion-exclusion principle.
Short note on the convolution of binomial coefficients
Rui Duarte, António Guedes de Oliveira
We know [Rui Duarte and António Guedes de Oliveira, New developments of an old identity, manuscript arXiv:1203.5424, submitted.] that, for every non-negative integer numbers $n,i,j…
New developments of an old identity
Rui Duarte, António Guedes de Oliveira
We give a direct combinatorial proof of a famous identity, by actually counting pairs of -subsets of -sets. Then we discuss t…
Constructions of bipartite and bipartite-regular hypermaps
Rui Duarte
A hypermap is bipartite if its set of flags can be divided into two parts A and B so that both A and B are the union of vertices, and consecutive vertices around an edge or a face…
Bipartite-uniform hypermaps on the sphere
Antonio Breda d'Azevedo, Rui Duarte
A hypermap is (hypervertex-) bipartite if its hypervertices can be 2-coloured in such a way that ``neighbouring'' hypervertices have different colours. It is bipartite-uniform if w…