Related papers: On counting plurifibered varieties
We give an account, in terms of fibered categories and their fibrewise duals, of aspects of the theory of bundle functors and star-bundle functors in differential geometry.
We consider the counting problem of the number of \textit{leaf-labeled increasing trees}, where internal nodes may have an arbitrary number of descendants. The set of all such trees is a discrete representation of the genealogies obtained…
We introduce {\it twist unimodal maps} of the interval and describe their structure. Sufficient conditions for the growth of over-rotation interval in families of maps are given.
Consider a density $f$ on $[0,1]$ that must be estimated from an i.i.d. sample $X_1,...,X_n$ drawn from $f$. In this note, we study binary-tree-based histogram estimates that use recursive splitting of intervals. If the decision to split an…
We give a formula and an estimation for the number of irreducible polynomials in two (or more) variables over a finite field.
We find surprisingly simple formulas for the limiting probability that the rank of a randomly selected vertex in a randomly selected phylogenetic tree or generalized phylogenetic tree is a given integer.
We present a new method to count unrooted maps on the sphere up to orientation-preserving homeomorphisms. The principle, called tree-decomposition, is to deform a map into an arborescent structure whose nodes are occupied by constrained…
The MULTICUT IN TREES problem consists in deciding, given a tree, a set of requests (i.e. paths in the tree) and an integer k, whether there exists a set of k edges cutting all the requests. This problem was shown to be FPT by Guo and…
SE Han's paper [11] discusses several variants of digital covering maps. We show several equivalences among these variants and discuss shortcomings in Han's paper.
We consider the problem of counting the number of possible sets of rankings (called ranking patterns) generated by unfolding models of codimension one. We express the ranking patterns as slices of the braid arrangement and show that all…
In enumerative combinatorics, it is often a goal to enumerate both labeled and unlabeled structures of a given type. The theory of combinatorial species is a novel toolset which provides a rigorous foundation for dealing with the…
We address the problem of existence of refined (i.e., depending on a formal parameter) tropical enumerative invariants, and we present two new examples of a refined count of rational marked tropical curves. One of the new invariants counts…
We identify the complexity of the classification problem for automorphisms of a given countable regularly branching tree up to conjugacy. We consider both the rooted and unrooted cases. Additionally, we calculate the complexity of the…
We consider the problem of enumerating the permutations containing exactly $k$ occurrences of a pattern of length 3. This enumeration has received a lot of interest recently, and there are a lot of known results. This paper presents an…
Any leafwise connection on a fibre bundle over a foliated manifold is proved to come from a connection on this fibre bundle.
The graph packing problem is a well-known area in graph theory. We consider a bipartite version and give almost tight conditions on the packability of two bipartite sequences.
We study the crossing-minimization problem in a layered graph drawing of planar-embedded rooted trees whose leaves have a given total order on the first layer, which adheres to the embedding of each individual tree. The task is then to…
From the perturbative expansion of the exact Green function, an exact counting formula is derived to determine the number of different types of connected Feynman diagrams. This formula coincides with the Arqu\`es-Walsh sequence formula in…
We use a well known problem in discrete and computational geometry (partitions of measures by $k$-fans) as a motivation and as a point of departure to illustrate many aspects, both theoretical and computational, of the problem of…
We provide upper bounds for the cardinality of the value set of a polynomial map in several variables over a finite field. These bounds generalize earlier bounds for univariate polynomials.