The cyclic sieving phenomenon: a survey

The cyclic sieving phenomenon was defined by Reiner, Stanton, and White in a 2004 paper. Let X be a finite set, C be a finite cyclic group acting on X, and f(q) be a polynomial in q with nonnegative integer coefficients. Then the triple (X,C,f(q)) exhibits the cyclic sieving phenomenon if, for all g in C, we have # X^g = f(w) where # denotes cardinality, X^g is the fixed point set of g, and w is a root of unity chosen to have the same order as g. It might seem improbable that substituting a root of unity into a polynomial with integer coefficients would have an enumerative meaning. But many instances of the cyclic sieving phenomenon have now been found. Furthermore, the proofs that this phenomenon hold often involve interesting and sometimes deep results from representation theory. We will survey the current literature on cyclic sieving, providing the necessary background about representations, Coxeter groups, and other algebraic aspects as needed.Comment: 48 pages, 3 figures, the sedcond version contains numerous changes suggested by colleagues and the referee. To appear in the London Mathematical Society Lecture Note Series. The third version has a few smaller change

On Pairs of Partitions with Steadily Decreasing Parts Communicated by George Andrews

AbstractA new generating function identity for special pairs of partitions with steadily decreasing parts is proved via a bijection. Viewing such pairs of partitions (or, more generally, special r-tuples of partitions) as coloured modular Young diagrams also allows to give bijective proofs for generating function identities due to Carlitz and Andrews

Explorative Graph Visualization

Netzwerkstrukturen (Graphen) sind heutzutage weit verbreitet. Ihre Untersuchung dient dazu, ein besseres Verständnis ihrer Struktur und der durch sie modellierten realen Aspekte zu gewinnen. Die Exploration solcher Netzwerke wird zumeist mit Visualisierungstechniken unterstützt. Ziel dieser Arbeit ist es, einen Überblick über die Probleme dieser Visualisierungen zu geben und konkrete Lösungsansätze aufzuzeigen. Dabei werden neue Visualisierungstechniken eingeführt, um den Nutzen der geführten Diskussion für die explorative Graphvisualisierung am konkreten Beispiel zu belegen.Network structures (graphs) have become a natural part of everyday life and their analysis helps to gain an understanding of their inherent structure and the real-world aspects thereby expressed. The exploration of graphs is largely supported and driven by visual means. The aim of this thesis is to give a comprehensive view on the problems associated with these visual means and to detail concrete solution approaches for them. Concrete visualization techniques are introduced to underline the value of this comprehensive discussion for supporting explorative graph visualization

The life and work of Prof. George Chrystal (1851-1911)

This thesis is principally concerned with George Chrystal's life and his work, mainly in three directions viz., as an experimentalist, a mathematician, and an educationist. The main object is to bring to light the work of a personality who is representative of many more who are always forgotten. The majority of historians of science consider the works of the giants in science, ignoring totally the contributions made by the less prominent people like Prof. George Chrystal. In fact their contributions serve as one of the most important factors in propagation of scientific knowledge. His main contributions: verification of Ohm's Law experimentally; Non-Euclidean geometry; differential equations; text books on algebra; theory of seiches; institution of leaving certificate examination in Scottish education and many more have been discussed in detail. A survey of Chrystal's general thought is given in so far as it may be gathered from his scattered remarks. The references are mentioned by numerals in the superscript, details of which are given at the end of each chapter. The main text consists of six chapters. There are three appendices at the end,' Appendix 'A' consists of his correspondence with different scientists, most of which is still unpublished. Appendix 'B' contains a bibliography of his contributions in chronological order, and Appendix 'C contains his three Promoter's addresses. Tables and figures are attached at their proper places, including some rarely available photographs

Prison or palace? Haven or hell? : an architectural and social study of the development of public lunatic asylums in Scotland, 1781-1930

In 1897 John Sibbald, Commissioner in Lunacy for Scotland, stated that ‘the construction of an asylum is a more interesting subject of study for the general reader than might be supposed.’ This thesis traces the development of the public asylum in Scotland from 1781 to 1930. By placing the institution in its wider social context it provides more than a historical account, exploring how the buildings functioned as well as giving an architectural analysis based on date, plan and style. Here the architecture represents more, and provides a physical expression of successive stages of public philanthropy and legislative changes during what was arguably one of the most rapidly evolving stages of history. At a time when few medical treatments were available, public asylum buildings created truly therapeutic environments, which allowed the mentally ill to live in relative peace and security. The thesis explores how public asylums in Scotland introduced the segregation or ‘classification’ of patients into separate needs-based groups under a system known as Moral Treatment. It focuses particularly on the evolving plan forms of these institutions from the earliest radial, prison-like structures to their development into self-sustaining village-style colonies and shows how the plan reflects new attitudes to treatment. While many have disappeared, the surviving Victorian and Edwardian mega-structures lie as haunting reminders of a largely forgotten era in Scottish psychiatry. Only a few of the original buildings are still in use today as specialist units, out-patient centres, and administrative offices for Scotland’s Health Boards. Others have been redeveloped as universities or luxury housing schemes, making use of the good-quality buildings and landscaping. Whatever their current use, public asylums stand today as an outward sign of the awakening of the Scottish people to the plight of the mentally ill in the nineteenth and early twentieth centuries

Fifty-second annual report of the receipts and expenditures of the city of Manchester, New Hampshire for the fiscal year ending December 31, 1897 together with other annual reports and papers relating to the affairs of the city.

This is an annual report containing vital statistics for a town/city in the state of New Hampshire

Fifty-second annual report of the receipts and expenditures of the city of Manchester, New Hampshire for the fiscal year ending December 31, 1897 together with other annual reports and papers relating to the affairs of the city.

This is an annual report containing vital statistics for a town/city in the state of New Hampshire