On the complexity of the chip-firing reachability problem

In this paper, we study the complexity of the chip-firing reachability problem. We show that for Eulerian digraphs, the reachability problem can be decided in strongly polynomial time, even if the digraph has multiple edges. We also show a special case when the reachability problem can be decided in polynomial time for general digraphs: if the target distribution is recurrent restricted to each strongly connected component. As a further positive result, we show that the chip-firing reachability problem is in co-NP for general digraphs. We also show that the chip-firing halting problem is in co-NP for Eulerian digraphs

Hypergraph polynomials and the Bernardi process

Recently O. Bernardi gave a formula for the Tutte polynomial $T(x,y)$ of a graph, based on spanning trees and activities just like the original definition, but using a fixed ribbon structure to order the set of edges in a different way for each tree. The interior polynomial $I$ is a generalization of $T(x,1)$ to hypergraphs. We supply a Bernardi-type description of $I$ using a ribbon structure on the underlying bipartite graph $G$. Our formula works because it is determined by the Ehrhart polynomial of the root polytope of $G$ in the same way as $I$ is. To prove this we interpret the Bernardi process as a way of dissecting the root polytope into simplices, along with a shelling order. We also show that our generalized Bernardi process gives a common extension of bijections (and their inverses) constructed by Baker and Wang between spanning trees and break divisors.Comment: 46 page

On the combinatorics of suffix arrays

We prove several combinatorial properties of suffix arrays, including a characterization of suffix arrays through a bijection with a certain well-defined class of permutations. Our approach is based on the characterization of Burrows-Wheeler arrays given in [1], that we apply by reducing suffix sorting to cyclic shift sorting through the use of an additional sentinel symbol. We show that the characterization of suffix arrays for a special case of binary alphabet given in [2] easily follows from our characterization. Based on our results, we also provide simple proofs for the enumeration results for suffix arrays, obtained in [3]. Our approach to characterizing suffix arrays is the first that exploits their relationship with Burrows-Wheeler permutations

The two-variable hypergraph Tutte polynomial via embedding activities

We prove that the two-variable Tutte polynomial of hypergraphs can be defined via embedding activities. We also prove that embedding activities of hypergraphs yield a Crapo-style decomposition of $\mathbb{Z}^E$, thus generalizing Bernardi's results from graphs to hypergraphs

Secondary succession of overgrazed Pannonian sandy grasslands

We assessed vegetation changes on acidic sandy soils in permanent plots to follow secondary succession after cessation of intensive goose breeding in E Hungary.We also aimed to estimate the time required for vegetation regeneration and indicate differences in secondary succession patterns at different altitudes in sand dunes. Two sites in the low and two in the high parts of the dunes were chosen and sampled for twelve years. The initial stages are characterized by ruderal communities dominated by nitrophilous annual weeds. Ruderal vegetation was soon replaced by nutrient-poor communities dominated by short-lived pioneer dicotyledonous plants and grasses. In the last few years of the study, coinciding with a rainy period, the low sites were dominated by the perennial grasses, Poa angustifolia, P. pratensis and Cynodon dactylon. In contrast, in the high sites a less dense cover of perennials developed. The influence of initial composition on vegetation development decreased with time and the influence of altitude increased during succession. The altitude of the site had a significant effect on regeneration. Species richness and Shannon diversity of the high sites increased during vegetation development and that of the lowsites decreased. Most annuals persisted in the high sites but became extinct in the low sites. The mean species turnover rate, irrespective of altitude, decreased during the study