Related papers: Labeled Chip-firing on Binary Trees with $2^n-1$ C…
We study three different kinds of embeddings of tree patterns: weakly-injective, ancestor-preserving, and lca-preserving. While each of them is often referred to as injective embedding, they form a proper hierarchy and their computational…
To a given gene tree topology $G$ and species tree topology $S$ with leaves labeled bijectively from a fixed set $X$, one can associate a set of ancestral configurations, each of which encodes a set of gene lineages that can be found at a…
We present algorithms for classification of linear codes over finite fields, based on canonical augmentation and on lattice point enumeration. We apply these algorithms to obtain classification results over fields with 2, 3 and 4 elements.…
We introduce ballot matrices, a signed combinatorial structure whose definition naturally follows from the generating function for labeled interval orders. A sign reversing involution on ballot matrices is defined. We show that matrices…
In mathematical phylogenetics, labeled histories describe the sequences by which sets of labeled lineages coalesce to a shared ancestral lineage. We study labeled histories for at-most-$r$-furcating trees. Consider a rooted leaf-labeled…
A string-like compact data structure for unlabelled rooted trees is given using 2n bits.
We present an algorithm for the classification of linear codes over finite fields, based on lattice point enumeration. We validate a correct implementation of our algorithm with known classification results from the literature, which we…
We provide a fundamental result for bucket increasing trees, which gives a complete characterization of all families of bucket increasing trees that can be generated by a tree evolution process. We also provide several equivalent…
Two classes of avalanche-finite matrices and their critical groups (integer cokernels) are studied from the viewpoint of chip-firing/sandpile dynamics, namely, the Cartan matrices of finite root systems and the McKay-Cartan matrices for…
This note is dedicated to presenting a polynomial analogue of $(n+1)!C_n=2^n(2n-1)!!$ (with $C_n$ as the $n$-th Catalan number) in the context of labeled plane trees and increasing plane trees, based on the definition of improper edges in…
Periodic trees are combinatorial structures which are in bijection with cluster tilting objects in cluster categories of affine type $\tilde{A}_{n-1}$. The internal edges of the tree encode the $c$-vectors corresponding to the cluster…
Partially ordered sets labeled with k labels (k-posets) and their homomorphisms are examined. We give a representation of directed graphs by k-posets; this provides a new proof of the universality of the homomorphism order of k-posets. This…
Labeled infinite trees provide combinatorial interpretations for many integer sequences generated by nested recurrence relations. Typically, such sequences are monotone increasing. Several of these sequences also have straightforward…
We investigate the problem of sequentially predicting the binary labels on the nodes of an arbitrary weighted graph. We show that, under a suitable parametrization of the problem, the optimal number of prediction mistakes can be…
We investigate the alternate order on a congruence-uniform lattice $\mathcal{L}$ as introduced by N. Reading, which we dub the core label order of $\mathcal{L}$. When $\mathcal{L}$ can be realized as a poset of regions of a simplicial…
We continue our studies of burn-off chip-firing games from [Discrete Math. Theor. Comput. Sci. 15 (2013), no. 1, 121-132; MR3040546] and [Australas. J. Combin. 68 (2017), no. 3, 330-345; MR3656659]. The latter article introduced randomness…
Tree sets are posets with additional structure that generalize tree-like objects in graphs, matroids, or other combinatorial structures. They are a special class of abstract separation systems. We study infinite tree sets and how they…
We consider so-called simple families of labelled trees, which contain, e.g., ordered, unordered, binary and cyclic labelled trees as special instances, and study the global and local behaviour of the number of inversions. In particular we…
We investigate the number of permutations that occur in random labellings of trees. This is a generalisation of the number of subpermutations occurring in a random permutation. It also generalises some recent results on the number of…
We study a partially ordered set of planar labeled rooted trees by use of combinatorial objects called Dyck tilings. A generating function of the poset is factorized when the minimum element of the poset is $312$-avoiding and satisfies some…