A note on higher-dimensional magic matrices

We provide exact and asymptotic formulae for the number of unrestricted, respectively indecomposable, $d$-dimensional matrices where the sum of all matrix entries with one coordinate fixed equals 2.Comment: AmS-LaTeX, 9 page

Galois groups of multivariate Tutte polynomials

The multivariate Tutte polynomial $\hat Z_M$ of a matroid $M$ is a generalization of the standard two-variable version, obtained by assigning a separate variable $v_e$ to each element $e$ of the ground set $E$. It encodes the full structure of $M$. Let \bv = \{v_e\}_{e\in E}, let $K$ be an arbitrary field, and suppose $M$ is connected. We show that $\hat Z_M$ is irreducible over K(\bv), and give three self-contained proofs that the Galois group of $\hat Z_M$ over K(\bv) is the symmetric group of degree $n$, where $n$ is the rank of $M$. An immediate consequence of this result is that the Galois group of the multivariate Tutte polynomial of any matroid is a direct product of symmetric groups. Finally, we conjecture a similar result for the standard Tutte polynomial of a connected matroid.Comment: 8 pages, final version, to appear in J. Alg. Comb. Substantial revisions, including the addition of two alternative proofs of the main resul

Partial pressure gauges

The determination of partial pressures in vacuum systems is usually performed by mass spectrometers. The most common type is the QMS. Quadrupole mass spectrometers were developed decades ago and have been used by vacuum specialists as a diagnostic tool since then. In the first part of the paper the principles of these mass spectrometers are briefly reviewed together with the key features of the instruments. This is necessary to operate these instruments. In the second part the boundary conditions which arise from the application as residual gas analyser in UHV/XHV plants are described. These lead to special versions of mass spectrometers. Results obtained with these instruments and typical artefacts in mass spectra obtained in the UHV are discussed