We analyze some enumerative and asymptotic properties of lattice paths below a line of
rational slope. We illustrate our approach with Dyck paths under a line of slope 2/5. This …

For $0\leq k\leq n-1$, we introduce a family of $ k $-skeletal paths which are counted by the
$ n $-th Catalan number for each $ k $, and specialize to Dyck paths when $ k= n-1$. We …

This thesis is concerned with the enumerative and asymptotic analysis of directed lattice
paths and tree-like structures. We introduce several new models and analyze some of their …

We analyze some enumerative and asymptotic properties of lattice paths below a line of
rational slope. We illustrate our approach with Dyck paths under a line of slope 2/5. This …

We analyse some enumerative and asymptotic properties of lattice paths below a line of
rational slope. We illustrate our approach with Dyck paths under a line of slope $2/5$. This …

This thesis is a compendium of three studies on which matroids and convex geometry play a
central role and show their connections to Catalan combinatorics, tiling theory, and …

We study a linear doubly indexed sequence that contains the Catalan numbers and relates
to a class of generalized Motzkin numbers. We obtain a closed form formula, a generating …