We consider walks on a triangular domain that is a subset of the triangular lattice. We then
specialise this by dividing the lattice into two directed sublattices with different weights. Our …

We propose a major index statistic on 01-fillings of moon polyominoes which, when
specialized to certain shapes, reduces to the major index for permutations and set partitions …

Several recent works have explored the deep structure between arc diagrams, their nestings
and crossings, and several other combinatorial objects including permutations, graphs …

There is a natural bijection between Dyck paths and basis diagrams of the Temperley–Lieb
algebra defined via tiling. Overhang paths are certain generalisations of Dyck paths allowing …

We give a bijection between partially directed paths in the symmetric wedge y=±x and
matchings, which sends north steps to nestings. This gives a bijective proof of a result of …

The combinatorial families of matchings, set partitions, permutations and graphs can each
be represented by a series of vertices along a horizontal line with arcs connecting them …

This thesis concerns the enumeration and structural properties of lattice paths. The study of
Dyck paths and their characteristics is a classical combinatorial subject. In particular, it is …

There is a natural bijection between Dyck paths and basis diagrams of the Temperley-Lieb
algebra defined via tiling. Overhang paths are certain generalisations of Dyck paths allowing …

There is a natural bijection between Dyck paths and basis diagrams of the Temperley–Lieb
algebra defined via tiling. Overhang paths are certain generalisations of Dyck paths allowing …