相关论文: On Ternary Trees and Fighting Fish
In this paper, we give a simple combinatorial explanation of a formula of A. Postnikov relating bicolored rooted trees to bicolored binary trees. We also present generalized formulas for the number of labeled k-ary trees, rooted labeled…
Taking a Feynman categorical perspective, several key aspects of the geometry of surfaces are deduced from combinatorial constructions with graphs. This provides a direct route from combinatorics of graphs to string topology operations via…
We study a class of combinatorial objects that we call "decorated trees". These consist of vertices, arrows and edges, where each edge is decorated by two integers (one near each of its endpoints), each arrow is decorated by an integer, and…
Tropical geometry with the max-plus algebra has been applied to statistical learning models over tree spaces because geometry with the tropical metric over tree spaces has some nice properties such as convexity in terms of the tropical…
We introduce two new binary operations with combinatorial species; the arithmetic product and the modified arithmetic product. The arithmetic product gives combinatorial meaning to the product of Dirichlet series and to the Lambert series…
The ongoing explosion of genome sequence data is transforming how we reconstruct and understand the histories of biological systems. Across biological scales, from individual cells to populations and species, trees-based models provide a…
This article focuses on a combinatorial structure specific to triangulated plane graphs with quadrangular outer face and no separating triangle, which are called irreducible triangulations. The structure has been introduced by Xin He under…
An evolutionary tree is a cascade of bifurcations starting from a single common root, generating a growing set of daughter species as time goes by. Species here is a general denomination for biological species, spoken languages or any other…
Object detection has found extensive applications in various tasks, but it is also susceptible to adversarial patch attacks. The ideal defense should be effective, efficient, easy to deploy, and capable of withstanding adaptive attacks. In…
Phylogenetic networks generalize phylogenetic trees by allowing the modelization of events of reticulate evolution. Among the different kinds of phylogenetic networks that have been proposed in the literature, the subclass of binary…
We present recursive formulas giving the maximal number of leaves in tree-like polyforms living in two-dimensional regular lattices and in tree-like polycubes in the three-dimensional cubic lattice. We call these tree-like polyforms and…
A graph can be regarded as an electrical network in which each edge is a resistor. This point of view relates combinatorial quantities, such as the number of spanning trees, to electrical ones such as effective resistance. The second and…
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 number of hook formulas and hook summation formulas have previously appeared, involving various classes of trees. One of these classes of trees is rooted trees with labelled vertices, in which the labels increase along every chain from…
We give a general construction of triangulations starting from a walk in the quarter plane with small steps, which is a discrete version of the mating of trees. We use a special instance of this construction to give a bijection between maps…
We introduce a new combinatorial structure: the metasylvester lattice on decreasing trees. It appears in the context of the $m$-Tamari lattices and other related $m$-generalizations. The metasylvester congruence has been recently introduced…
In the Firefighter problem, introduced by Hartnell in 1995, a fire spreads through a graph while a player chooses which vertices to protect in order to contain it. In this paper, we focus on the case of trees and we consider as well the…
In this paper, we present a simplified framework to represent competition, coordination and bargaining in fisheries when they operate under financial and technological constraints. Competition within constraints leads to a particular type…
A di-sk tree is a rooted binary tree whose nodes are labeled by $\oplus$ or $\ominus$, and no node has the same label as its right child. The di-sk trees are in natural bijection with separable permutations. We construct a combinatorial…
We give series solutions to single insertion place propagator-type systems of Dyson--Schwinger equations using binary tubings of rooted trees. These solutions are combinatorially transparent in the sense that each tubing has a…