Algebraic matroids and Frobenius flocks

We show that each algebraic representation of a matroid $M$ in positive characteristic determines a matroid valuation of $M$, which we have named the {\em Lindstr\"om valuation}. If this valuation is trivial, then a linear representation of $M$ in characteristic $p$ can be derived from the algebraic representation. Thus, so-called rigid matroids, which only admit trivial valuations, are algebraic in positive characteristic $p$ if and only if they are linear in characteristic $p$. To construct the Lindstr\"om valuation, we introduce new matroid representations called flocks, and show that each algebraic representation of a matroid induces flock representations.Comment: 21 pages, 1 figur

Are Hand Preference and Sexual Orientation Possible Predicting Factors for Finasteride Adverse Effects in Male Androgenic Alopecia?

Sexual side effects of finasteride seem to be redoubtable, being encountered not only during therapy but also after treatment cessation. Consequently, any possible clinical/paraclinical elements that might predict these adverse effects would be useful in the selection of a therapeutic strategy for male androgenic alopecia. Previous published studies show that some compounds that interfere with sexual hormones can decrease sexual activation and response, according to hand preference (as reported for finasteride and tamoxifen) and according to sexual orientation (as noted for bicalutamide). Our preliminary published data and the arguments presented here suggest that these two individual parameters might be used by dermatologists in the therapeutic approach of male androgenic alopecia, so as to alert specific subsets of men, prior to treatment, of the potential increased risk for developing adverse effects to finasteride

Determinants of (generalised) Catalan numbers

We show that recent determinant evaluations involving Catalan numbers and generalisations thereof have most convenient explanations by combining the Lindstr\"om-Gessel-Viennot theorem on non-intersecting lattice paths with a simple determinant lemma from [Manuscripta Math. 69 (1990), 173-202]. This approach leads also naturally to extensions and generalisations.Comment: AmS-TeX, 16 pages; minor correction

Enumeration of tilings of quartered Aztec rectangles

We generalize a theorem of W. Jockusch and J. Propp on quartered Aztec diamonds by enumerating the tilings of quartered Aztec rectangles. We use subgraph replacement method to transform the dual graph of a quartered Aztec rectangle to the dual graph of a quartered lozenge hexagon, and then use Lindstr\"{o}m-Gessel-Viennot methodology to find the number of tilings of a quartered lozenge hexagon.Comment: 28 page