6 citations · 16 across the 7 of their papers we have counts for
7 papers
Generating functions of lattice paths
Rui Duarte, António Guedes de Oliveira
We recall the main types of lattice paths, which are sequences in the lattice of integer coordinates points in the plane. We start with the fundamental central lattice paths and Dy…
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…