Related papers: Cyclic sieving phenomena for trees and tree-rooted…
In 2010, B. Rhoades proved that promotion together with the fake-degree polynomial associated with rectangular standard Young tableaux give an instance of the cyclic sieving phenomenon. We extend this result to all skew standard Young…
This paper presents our studies on the rearrangement of links from the structure of websites for the purpose of improving the valuation of a page or group of pages as established by a ranking function as Google's PageRank. We build our…
A caterpillar tree is a connected, acyclic, graph in which all vertices are either a member of a central path, or joined to that central path by a single edge. In other words, caterpillar trees are the class of trees which become path…
A non-local model describing the growth of a tree-like transportation network with given allocation rules is proposed. In this model we focus on tree like networks, and the network transports the very resource it needs to build itself. Some…
Random spanning trees are among the most prominent determinantal point processes. We give four examples of random spanning trees on ladder-like graphs whose rungs form stationary renewal processes or regenerative processes of order two,…
Dynamic trees are mixtures of tree structured belief networks. They solve some of the problems of fixed tree networks at the cost of making exact inference intractable. For this reason approximate methods such as sampling or mean field…
We introduce some natural families of distributions on rooted binary ranked plane trees with a view toward unifying ideas from various fields, including macroevolution, epidemiology, computational group theory, search algorithms and other…
Tree-like tableaux are combinatorial objects that appear in a combinatorial understanding of the PASEP model from statistical mechanics. In this understanding, the corners of the Southeast border correspond to the locations where a particle…
A rotor-router walk on a graph is a deterministic process, in which each vertex is endowed with a rotor that points to one of the neighbors. A particle located at some vertex first rotates the rotor in a prescribed order, and then it is…
In this paper, we study tree--like tableaux, combinatorial objects which exhibit a natural tree structure and are connected to the partially asymmetric simple exclusion process (PASEP). There was a conjecture made on the total number of…
Signs of hierarchy are prevalent in a wide range of systems in nature and society. One of the key problems is quantifying the importance of hierarchical organisation in the structure of the network representing the interactions or…
Tree-child networks are a recently-described class of directed acyclic graphs that have risen to prominence in phylogenetics (the study of evolutionary trees and networks). Although these networks have a number of attractive mathematical…
The number of embeddings of a partially ordered set $S$ in a partially ordered set $T$ is the number of subposets of $T$ isomorphic to $S$. If both, $S$ and $T$, have only one unique maximal element, we define good embeddings as those in…
We study tree-to-tree transformations that can be defined in first-order logic or monadic second-order logic. We prove a decomposition theorem, which shows that every transformation can be obtained from prime transformations, such as…
We prove a general result about the decomposition on ergodic components of group actions on boundaries of spherically homogeneous rooted trees. Namely, we identify the space of ergodic components with the boundary of the orbit tree…
A decision tree looks like a simple directed acyclic computational graph, where only the leaf nodes specify the output values and the non-terminals specify their tests or split conditions. From the numerical perspective, we express decision…
A new ``Percolation with Clustering'' (PWC) model is introduced, where (the probabilities of) site percolation configurations on the leaf set of a binary tree are rewarded exponentially according to a generic function, which measures the…
Rooted phylogenetic networks are used by biologists to infer and represent complex evolutionary relationships between species that cannot be accurately explained by a phylogenetic tree. Tree-child networks are a particular class of rooted…
To investigate the topological structure of Morse flows with a sink on the 2-sphere we use the planar tree as complete topological invariant of the flow. We give a list of all planar tree with at least 7 edges. We use a list of rooted…
Given a rooted tree and a ranking of its leaves, what is the minimum number of inversions of the leaves that can be attained by ordering the tree? This variation of the problem of counting inversions in arrays originated in mathematical…