972 research outputs found
Enumerative sequences of leaves and nodes in rational trees
International audienc
Refined descendant invariants of toric surfaces
We construct refined tropical enumerative genus zero invariants of toric
surfaces that specialize to the tropical descendant genus zero invariants
introduced by Markwig and Rau when the quantum parameter tends to . In the
case of trivalent tropical curves our invariants turn to be the
Goettsche-Schroeter refined broccoli invariants. We show that this is the only
possible refinement of the Markwig-Rau descendant invariants that generalizes
the Goettsche-Schroeter refined broccoli invariants. We discuss also the
computational aspect (a lattice path algorithm) and exhibit some examples.Comment: 30 pages, 7 figures; matches the published versio
A-Tint: A polymake extension for algorithmic tropical intersection theory
In this paper we study algorithmic aspects of tropical intersection theory.
We analyse how divisors and intersection products on tropical cycles can
actually be computed using polyhedral geometry. The main focus of this paper is
the study of moduli spaces, where the underlying combinatorics of the varieties
involved allow a much more efficient way of computing certain tropical cycles.
The algorithms discussed here have been implemented in an extension for
polymake, a software for polyhedral computations.Comment: 32 pages, 5 figures, 4 tables. Second version: Revised version, to be
published in European Journal of Combinatoric
Non-Contiguous Pattern Avoidance in Binary Trees
In this paper we consider the enumeration of binary trees avoiding
non-contiguous binary tree patterns. We begin by computing closed formulas for
the number of trees avoiding a single binary tree pattern with 4 or fewer
leaves and compare these results to analogous work for contiguous tree
patterns. Next, we give an explicit generating function that counts binary
trees avoiding a single non-contiguous tree pattern according to number of
leaves. In addition, we enumerate binary trees that simultaneously avoid more
than one tree pattern. Finally, we explore connections between pattern-avoiding
trees and pattern-avoiding permutations.Comment: 21 pages, 2 figures, 1 tabl
Enumerative Combinatorics
Enumerative Combinatorics focusses on the exact and asymptotic counting of combinatorial objects. It is strongly connected to the probabilistic analysis of large combinatorial structures and has fruitful connections to several disciplines, including statistical physics, algebraic combinatorics, graph theory and computer science. This workshop brought together experts from all these various fields, including also computer algebra, with the goal of promoting cooperation and interaction among researchers with largely varying backgrounds
- …