Related papers: Height restricted lattice paths, Elenas, and bijec…
The in-order traversal provides a natural correspondence between binary trees with a decreasing vertex labeling and endofunctions on a finite set. By suitably restricting the vertex labeling we arrive at a class of trees that we call…
Dyck tilings are certain tilings in the region surrounded by two Dyck paths. We study bijections and combinatorial objects bijective to Dyck tilings, which include Dyck tiling strip (DTS) and Dyck tiling ribbon (DTR) bijections, increasing…
Various lattice path models are reviewed. The enumeration is done using generating functions. A few bijective considerations are woven in as well. The kernel method is often used. Computer algebra was an essential tool. Some results are…
The ternary betweenness relation of a tree, B(x,y,z) expresses that y is on the unique path between x and z. This notion can be extended to order-theoretic trees defined as partial orders such that the set of nodes larger than any node is…
The dual of a map is a fundamental construction on combinatorial maps, but many other combinatorial objects also possess their notion of duality. For instance, the Tamari lattice is isomorphic to its order dual, which induces an involution…
A hypergraph consists of a set of vertices and a set of subsets of vertices, called hyperedges. In the metro map metaphor, each hyperedge is represented by a path (the metro line) and the union of all these paths is the support graph (metro…
This work considers lattice walks restricted to the quarter plane, with steps taken from a set of cardinality three. We present a complete classification of the generating functions of these walks with respect to the classes algebraic,…
In this paper, we give a bijection between rooted labeled ordered forests with a selected subset of their leaves and the regions of the type $C$ Catalan arrangement in $\R^n$. We thus obtain a bijective proof of the well-known enumeration…
The Stanley lattice, Tamari lattice and Kreweras lattice are three remarkable orders defined on the set of Catalan objects of a given size. These lattices are ordered by inclusion: the Stanley lattice is an extension of the Tamari lattice…
We show that the Chow covectors of a linkage matching field define a bijection between certain degree vectors and lattice points, and we demonstrate how one can recover the linkage matching field from this bijection. This resolves two open…
Each labeled rooted tree is associated with a hyperplane arrangement, which is free with exponents given by the depths of the vertices of this tree. The intersection lattices of these arrangements are described through posets of forests.…
Given a tree $T$, its path polytope is the convex hull of the edge indicator vectors for the paths between any two distinct leaves in $T$. These polytopes arise naturally in polyhedral geometry and applications, such as phylogenetics,…
It is known when we call a poset P, a $\mathcal{P}$-chain permutational poset, given a subset of permutations $\mathcal{P}$ of the symmetric group $S_{n}$. In this work, we use the same idea to study subsets of words of length $n$, that are…
In this paper, we study the problem of constructing a network by observing ordered connectivity constraints, which we define herein. These ordered constraints are made to capture realistic properties of real-world problems that are not…
An ordered labeled tree is a tree in which the nodes are labeled and the left-to-right order among siblings is relevant. The edit distance between two ordered labeled trees is the minimum cost of changing one tree into the other through a…
Trying to enumerate all of the walks in a 2D lattice is a fun combinatorial problem and there are numerous applications, from polymers to sports. Computers provide a wonderful tool for analyzing these walks; we provide a Maple package for…
We introduce a bijection between inequivalent minimal factorizations of the n-cycle (1 2 ... n) into a product of smaller cycles of given length, on one side, and trees of a certain structure on the other. We use this bijection to count the…
We investigate the definability (reducts) lattice of the order of integers and describe a sublattice generated by relations 'between', 'cycle', 'separation', 'neighbor', '1-codirection', 'order' and equality'. Some open questions are…
This paper deals with the problem of finding the preferred extensions of an argumentation framework by means of a bijection with the naive sets of another framework. First, we consider the case where an argumentation framework is…
We introduce the set of (non-spanning) tree-decorated planar maps, and show that they are in bijection with the Cartesian product between the set of trees and the set of maps with a simple boundary. As a consequence, we count the number of…