Structure and enumeration of (3+1)-free posets

A poset is (3+1)-free if it does not contain the disjoint union of chains of length 3 and 1 as an induced subposet. These posets play a central role in the (3+1)-free conjecture of Stanley and Stembridge. Lewis and Zhang have enumerated (3+1)-free posets in the graded case by decomposing them into bipartite graphs, but until now the general enumeration problem has remained open. We give a finer decomposition into bipartite graphs which applies to all (3+1)-free posets and obtain generating functions which count (3+1)-free posets with labelled or unlabelled vertices. Using this decomposition, we obtain a decomposition of the automorphism group and asymptotics for the number of (3+1)-free posets.Comment: 28 pages, 5 figures. New version includes substantial changes to clarify the construction of skeleta and the enumeration. An extended abstract of this paper appears as arXiv:1212.535

Installation of insecticide-treated durable wall lining: evaluation of attachment materials and product durability under field conditions.

BACKGROUND: Insecticide-treated durable wall lining (DL) is a new method of vector control designed to supplement LLINs and overcome two inherent limitations of LLINs and IRS: nightly behavioural compliance and short residual activity, respectively. DL is a deltamethrin-treated polyethylene material, which when used to cover interior house walls, functions as long-lasting IRS. Because the DL concept anticipates minimal upkeep, a primary challenge is how to guarantee correct household installation and in situ longevity for several years. Field trials were undertaken on various wall surfaces in Ghana to identify a logistically feasible, durable and re-usable method for DL wall attachment and to pilot new methods for assessing DL durability. METHODS: Over fifty-five candidate attachment or fixing products, including mechanical fasteners, material anchors and adhesives, were evaluated for their ability to tolerate static loads (simulating long-term installation) and short-term heavy weights (imitating shock damage). Attachment products were also scored using qualitative logistical and feasibility criteria, including ease of preparation, grip of fixing to DL and possibility of re-use. RESULTS: The stress tests provided a standardised, reproducible and reliable system for assessing fixing effectiveness and DL durability, with 64% (14/22) of adhesives and 15% (2/13) of mechanical fasteners failing to meet the minimum requirements of attaching DL to mud walls for set time periods. For most fixings, less outward load (0.2-8.0 kg) was required to detach DL from the wall, compared to downward load (0.2-19.2 kg). Fixings were better able to grip DL onto concrete than clay surfaces. Using a plastic nail cap to increase DL attachment area greatly improved grip and outward load tolerance, more so than varying nail size, length or texture. CONCLUSIONS: Based on a series of systematic stress tests, optimized fixing products for polyethylene DL wall attachment were identified. In parallel, a detailed and adaptable method of DL household installation was developed for routine deployment in malaria endemic areas. These standardized stress tests will form the basis for comparative evaluations of new types of DL textile, which incorporate non-pyrethroid insecticides to control malaria transmitted by resistant mosquito populations