This paper is an initial inquiry into the structure of the Hopf algebra of matroids with restriction-contraction coproduct. Using a family of matroids introduced by Crapo in 1965, we show that the subalgebra generated by a single point and a single loop in the dual of this Hopf algebra is free.
We introduce a noncommutative binary operation on matroids, called free product. We show that this operation respects matroid duality, and has the property that, given only the cardinalities, an ordered pair of matroids may be recovered, up to isomorphism, from its free product. We use these results to give a short proof of Welsh's 1969 conjecture, which… (More)
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We report the results of whole-genome transcriptional profiling of the light-to-dark transition with the model photosynthetic prokaryote Synechocystis sp. strain PCC 6803 (Synechocystis). Experiments were conducted by growing Synechocystis cultures to mid-exponential phase and then exposing them to two cycles of light/dark conditions, during which RNA… (More)
We study the combinatorial, algebraic and geometric properties of the free product operation on matroids. After giving cryptomorphic definitions of free product in terms of independent sets, bases, circuits, closure, flats and rank function, we show that free product, which is a noncommutative operation, is associative and respects matroid duality. The free… (More)
Research on psychopathy in women has generated equivocal laboratory findings. This study examined the performance of psychopathic women in 2 laboratory tasks designed to assess abnormal selective attention associated with response modulation deficits: a computerized picture–word (PW) task, and a picture–word Stroop (PW Stroop) task. Consistent with data… (More)
Recent attempts to validate the Psychopathy Checklist—Revised (PCL-R; R. D. Hare, 1991) as a measure of psychopathy in female offenders have been limited by a failure to examine laboratory correlates of the syndrome. We assessed 112 incarcerated women by using the PCL-R and examined their performance on a card perseveration task that has been used to… (More)
We outline an approach to enumeration problems which relies on the algebra of free abelian groups, giving as our main application a generalisa-tion of the chromatic polynomial of a simple graph G. Our polynomial lies in the free abelian group generated by the poset K(G) of contractions of G, and reduces to the classical case after a simple substitution. Its… (More)