Logarithms of iteration matrices, and proof of a conjecture by Shadrin and Zvonkine

A proof for a conjecture by Shadrin and Zvonkine, relating the entries of a matrix arising in the study of Hurwitz numbers to a certain sequence of rational numbers, is given. The main tools used are iteration matrices of formal power series and their (matrix) logarithms.Comment: 29 p

Residual properties of graph manifold groups

Let $f\colon M\to N$ be a continuous map between closed irreducible graph manifolds with infinite fundamental group. Perron and Shalen showed that if $f$ induces a homology equivalence on all finite covers, then $f$ is in fact homotopic to a homeomorphism. Their proof used the statement that every graph manifold is finitely covered by a $3$-manifold whose fundamental group is residually $p$ for every prime $p$. We will show that this statement regarding graph manifold groups is not true in general, but we will show how to modify the argument of Perron and Shalen to recover their main result. As a by-product we will determine all semidirect products $\Z \ltimes \Z^d$ which are residually $p$ for every prime $p$

A criterion for HNN extensions of finite pp-groups to be residually pp

We give a criterion for an HNN extension of a finite $p$-group to be residually $p$.Comment: 14

Finiteness theorems in stochastic integer programming

We study Graver test sets for families of linear multi-stage stochastic integer programs with varying number of scenarios. We show that these test sets can be decomposed into finitely many ``building blocks'', independent of the number of scenarios, and we give an effective procedure to compute these building blocks. The paper includes an introduction to Nash-Williams' theory of better-quasi-orderings, which is used to show termination of our algorithm. We also apply this theory to finiteness results for Hilbert functions.Comment: 36 p