Related papers: Fighting Fish: enumerative properties
Fighting fish is a combinatorial configuration introduced by Duchi et al. as a new model of branching surfaces that generalizes directed convex polyominoes. We come up with an alternative construction of fighting fish, using a tree…
We introduce extended fighting fish as branching surfaces that can also be seen as walks in the quarter plane defined by simple rewriting rules. The main result we present in the article is a direct bijection between extended fighting fish…
In 2017, Duchi, Guerrini, Rinaldi and Schaeffer proposed a new family of combinatorial objects called "fighting fish", which are counted by the same formula as more classical objects, such as two-stack sortable permutations and…
The class of fighting fish is a recently introduced model of branching surfaces generalizing parallelogram polyominoes. We can alternatively see them as gluings of cells, walks on the square lattice confined to the quadrant or shuffle of…
This paper conducts a numerical study of a geometrical structure called $\epsilon$-school for predator-avoidance fish schools, based on our previous mathematical model. Our results show that during a predator attack, the number of…
Collective behaviour in living systems is observed across many scales, from bacteria to insects, to fish shoals. Zebrafish have emerged as a model system amenable to laboratory study. Here we report a three-dimensional study of the…
Islands are combinatorial objects that can be intuitively defined on a board consisting of a finite number of cells. Based on the neighbor relation of the cells, it is a fundamental property that two islands are either containing or…
A triangular partition is a partition whose Ferrers diagram can be separated from its complement (as a subset of $\mathbb{N}^2$) by a straight line. Having their origins in combinatorial number theory and computer vision, triangular…
Given a complete graph with positive weights on its edges, we define the weight of a subset of edges as the product of weights of the edges in the subset and consider sums (partition functions) of weights over subsets of various kinds:…
We discuss a cellular automata model to study the competition between an emergent better fitted species against an existing majority species. The model implement local fights among small group of individual and a synchronous random walk on…
We present a novel model of stochastic differential equations for foraging behavior of fish schools in space including obstacles. We then study the model numerically. Three configurations of space with different locations of food resource…
A filter lattice is a distributive lattice formed by all filters of a poset in the anti-inclusion order. We study the combinatorial properties of the Hasse diagrams of filter lattices of certain posets, so called Fibonacci-like cubes, in…
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…
We prove an identity for five arguments, valid in the lattice of natural numbers with gcd and lcm as lattice operations. More generally, this identity characterizes arbitrary distributive lattices. Fixing three of the five arguments, we…
The thrust benefits of lateral configurations of two-dimensional undulating fish-like bodies are investigated using high-fidelity numerical simulation. The solution of the Navier--Stokes equations is carried out with a viscous vortex…
We establish an equivalence between a family of adversarial training problems for non-parametric binary classification and a family of regularized risk minimization problems where the regularizer is a nonlocal perimeter functional. The…
We look at buildings' competition over space in cities through the lens of ecology. Adopting the convex hull of the building's footprint perimeter as a definition of species yields parallels to forest trees' competition, which we expound…
Several articles deal with tilings with various shapes, and also a very frequent type of combinatorics is to examine the walks on graphs or on grids. We combine these two things and give the numbers of the shortest walks crossing the tiled…
In undulatory swimming of fish, muscles contract sequentially along the body to generate a bending wave that pushes against the water and produces thrust. Here, we use a 3D computational fluid dynamics model coupled to the motion of the…
In [2], while studying a relevant class of polyominoes that tile the plane by translation, i.e., double square polyominoes, the authors found that their boundary words, encoded by the Freeman chain coding on a four letters alphabet, have…