Partially directed snake polyominoes

TL;DR: This work presents recursive formulas giving the maximal number of leaves in tree-like polyforms living in two-dimensional regular lattices and in Tree-likepolycubes in the three-dimensional cubic lattice, and focuses on the particular case of polyforms and polycubes, that is the family of fully leafed structures that maximize the ratio (number of leaves) / ( number of cells) .

TL;DR: In this paper, the enumeration of two subfamilies of the family of snake polyominoes, stairs and snakes of height 2, was studied from a graph theoretical perspective, using classical ideas, as symmetries, and a new approach that connects these snakes with the partitions of integers.

TL;DR: In this paper, a relation between MZF and Dirichlet generating function of parallelogram polyominoes was established, and an explicit formula and an ordinary generating function was given for polycubes according to their width, length and depth.

TL;DR: In this article, the enumeration of plane lattice walks with steps in S, that start from (0, 0) and always remain in the first quadrant of S, is studied.

TL;DR: This work enumerates (by their site-perimeter) the simplest family of polyominoes that are not fully convex-bargraphs, a type that has never been encountered so far in the combinatorics literature: a q-series into which an algebraic series has been substituted.

TL;DR: In this paper, the enumeration of plane lattice walks with steps in S, that start from (0, 0) and remain in the first quadrant {(i, j) : i 0, j 0}.

TL;DR: The art of combinatorial proof has been studied extensively in the literature, e.g. as mentioned in this paper. But their work is focused on proving that really counts: The Art of Combinatorial Proof.