On Generalized Delannoy Paths

Propositional Goedel Logic and Delannoy Paths

Generalizing Delannoy Numbers via Counting Weighted Lattice Paths

The aim of this paper is to introduce a generalization of Delannoy numbers. The standard Delannoy numbers count lattice paths from (0, 0) to (n, k) consisting of horizontal (1, 0), vertical (0, 1), and diagonal (1, 1) steps called segments. We assign weights to the segments of the lattice paths, and we sum weights of all lattice paths from any (a, b) to (n, k). Generating functions for the gene...

On Generalized Dyck Paths

We generalize the elegant bijective proof of the Chung Feller theorem from the paper of Young-Ming Chen [The Chung-Feller theorem revisited, Disc. Math. 308 (2008), 1328–1329].

Returns and Hills on Generalized Dyck Paths

In 2009, Shapiro posed the following question: “What is the asymptotic proportion of Dyck paths having an even number of hills?” In this paper, we answer Shapiro’s question, as well as a generalization of the question to ternary paths. We find that the probability that a randomly chosen ternary path has an even number of hills approaches 125/169 as the length of the path approaches infinity. Ou...

Generalized Source Shortest Paths on Polyhedral Surfaces

We present an algorithm for computing shortest paths and distances from a single generalized source (point, segment, polygonal chain or polygon) to any query point on a possibly non-convex polyhedral surface. The algorithm also handles the case in which polygonal chain or polygon obstacles on the polyhedral surface are allowed. Moreover, it easily extends to the case of several generalized sour...