A polyhedral model of partitions with bounded differences and a bijective proof of a theorem of Andrews, Beck, and Robbins

The main result of this paper is a bijective proof showing that the generating function for partitions with bounded differences between largest and smallest part is a rational function. This result is similar to the closely related case of partitions with fixed differences between largest and smallest parts which has recently been studied through analytic methods by Andrews, Beck, and Robbins. Our approach is geometric: We model partitions with bounded differences as lattice points in an infinite union of polyhedral cones. Surprisingly, this infinite union tiles a single simplicial cone. This construction then leads to a bijection that can be interpreted on a purely combinatorial level.Comment: 12 pages, 5 figure

On the equivariant cohomology of rotation groups and Stiefel manifolds

AbstractIn this paper, we compute the RO(Z/2)-graded equivariant cohomology of rotation groups and Stiefel manifolds with particular involutions

Effects of the COVID-19 Pandemic on Logging Contractors in Sweden: A Survey on Personnel Absenteeism, Safety Measures and Economic Impacts

Forestry contractors perform the majority of forestry work in Sweden. Many contractors have small financial margins and may therefore be sensitive to disturbances. Recent years have been extraordinary due to the COVID-19 pandemic, and the objective of this study was to clarify how Swedish logging contractors were affected by it. In 2022, a survey was sent to 1175 companies registered to perform logging, and finally, the responses of 205 contractors were analyzed. The results show that 32% of the contractors experienced a higher absence of personnel during the pandemic. A correlation between the number of employees and the degree to which the company suffered from personnel absenteeism was identified. The majority of contractors implemented safety measures to reduce the risk of infection, usually concerning personal hygiene and social contacts in the workplace. At the time of the study, 51% of the logging contractors perceived that their financial situation was worse than before the pandemic, with those primarily engaged in logging having been hit harder than those with a more varied range of services. The study concludes that, overall, the contractors seem to have handled the pandemic quite well, but high fuel prices and inflation pose major challenges to their finances

On the Equivariant Cohomology of Rotation Groups and Stiefel Manifolds

In this paper, we compute the RO(Z/2)-graded equivariant cohomology of rotation groups and Stiefel manifolds with particular involutions

Non-industrial Private Forest Owners' Knowledge and Forest Management Preferences Regarding Forest Damage in Northern Sweden

In northern Sweden, large forest areas are affected by extensive damage caused by moose, fungi, beetle and other biological pests. For non-industrial private forest (NIPF) owners this leads to large losses of value, not only in economic terms but also in the form of loss of biodiversity and amenity values. Therefore, several research projects are underway to develop new silvicultural methods and other measures to reduce damage. However, a successful implementation of these will often depend on the willingness and knowledge of the forest owners. The objective of this study was, therefore, to elucidate NIPF owners' knowledge about forest damage and their preferences regarding forest management alternatives that potentially could mitigate the damage situation. Data were collected through a questionnaire that was distributed to a random sample of 1,177 NIPF owners in northern Sweden, and the response rate was 31% (n = 368). The results show that 19% of the NIPF owners did not know the current damage situation in their own forest. In addition, NIPF owners judged that their knowledge to identify damage themselves is quite limited, except for damage caused by moose. Regarding future management options, many were positive towards avoiding clear-cuts in suitable areas, while many were negative towards implementing alternative tree species such as larch and lodgepole pine. The study concludes that there is a clear need to inform and educate NIPF owners about forest damage, but also that there will be challenges in reaching all types of owners

Genetics of local adaptation in Arabidopsis thaliana - seed dormancy as a case study

Local adaptation occurs when natural selection favours different phenotypes in different locations. Here, I studied the genetics of adaptation using local adaptation for seed dormancy in Arabidopsis thaliana as a model system. I asked, is there local adaptation for seed dormancy and what environmental factors drive it? What is the genetic basis of adaptation and what is the molecular nature of adaptive changes? To answer these questions I conducted a population genetic study, comparing neutral markers, candidate genes and traits. Some QTL-mapping experiments were also performed. The results obtained indicate that there is local adaptation in seed dormancy and this is mediated by the amount of precipitation received during the summer months. Local adaptation seems to occur at a regional geographic scale. Based on genetic mapping and studies, the large effect gene DOG1 is mainly responsible for adaptation, together with several other loci with minor effects. A population genetic study of DOG1 revealed that there is a signature of local selection on DOG1. Several functional alleles of DOG1 are segregating in natural populations. Mutations that increase or decrease dormancy seem to have occurred several times independently. This likely happens because of a low migration rate, new mutations occur in separate populations but they cannot migrate efficiently to other populations and thus no single mutation becomes fixed. The molecular basis of adaptive changes could not be determined, yet some candidate mutations for functional changes were identified. In addition, some of the results raised concerns about the proper way to estimate genetic differentiation. Therefore, the statistical properties of some estimators of genetic differentiation were studied using computer simulations. An estimator that takes mutation model into account can be used to compare different types of markers

On the equivariant cohomology of rotation groups and Stiefel manifolds

In this paper, we compute the $RO(\mathbb{Z}/2)$-graded equivariant cohomology of rotation groups and Stiefel manifolds with particular involutions

A Freeness Theorem for RO(Z/2)-graded Cohomology

In this paper it is shown that the RO(Z/2)-graded cohomology of a certain class of Rep(Z/2)-complexes, which includes projective spaces and Grassmann manifolds, is always free as a module over the cohomology of a point when the coefficient Mackey functor is \underline{Z/2}