The symmetry of intersection numbers in group theory

For suitable subgroups of a finitely generated group, we define the intersection number of one subgroup with another subgroup and show that this number is symmetric. We also give an interpretation of this number.Comment: 19 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol2/paper2.abs.html . Includes erratum added to the original, published 19 Mar 199

Introducing Electronic Information Services to First-Year Composition Students: Pedagogical and Practical Concerns

More and more of the college and university library\u27s resources are becoming computerized. As first year students enter the library, they are often confronted with an overwhelming array of computer terminals and workstations. While some students are avid computer users, others are fearful or intimidated. Regardless of one\u27s proclivity towards electronic resources and services, the first year student must learn how to evaluate the relevancy of each of the various systems to their own research needs and make a selection that is best suited to their particular tasks. This presentation will review general considerations and guidelines for including electronic library resources into the research component of first year composition classes. Introducing computerized databases into the research process presents numerous challenges to the composition instructor. Parting from the traditional research strategies often presented in the published research guides may lead the instructor into uncharted territories. Yet, the availability of electronic sources has become so prolific that ignoring them or minimizing their use would be an extreme disservice to the students. CD-ROM technology and locally mounted databases have brought sophisticated searching capabilities into the hands of the entire university community, including first year undergraduates. A strong research component in the first year writing course can provide a firm foundation on which advanced thinking and writing skills can develop. While the vast array of electronic resources may present exciting or intriguing possibilities, instructors must be careful not to overwhelm the students with too much or to present online systems as the best answer for every research need. Putting these electronic resources into an appropriate context for the beginning researcher is paramount to teaching their effective utilization. A thorough presentation of the research process, with its conceptual underpinnings and strategies, provides the broad framework within which these resources may be most effectively utilized. In this presentation I will discuss selecting databases and using electronic resources in the introductory level composition course. A close working relationship with the instruction librarian will help to ensure adequate coverage of electronic services for the novice researcher and maintain an appropriate balance with print sources as well. While taking advantage of the improved access to information through electronic means, educators must integrate critical thinking and evaluative skills throughout the students\u27 research and writing processes. The many options available in our information-rich society force us to make choices, and we must help the first year students realize that computer, though it may provide opportunity, does not always mean best

The Hopf monoid on nonnesting supercharacters of pattern groups

We construct supercharacter theories for a collection of unipotent matrix groups and produce a Hopf monoid from the supercharacters. These supercharacter theories are coarser than those defined by Diaconis--Isaacs for algebra groups and have supercharacters and superclasses indexed by nonnesting labeled set partitions. We compute the supercharacter tables and describe the product and coproduct of the Hopf monoid combinatorially. We also show that this Hopf monoid is free.Comment: Final version; DOI adde

Urban geography: urban growth machine

Urban growth machine is an influential thesis of urban politics that suggests the objective of growth unites otherwise pluralistic interests in relation to a city. The thesis is situated within a broader theory about the commodification of place, where place is understood to be socially and economically valued land. Its key premise is that coalitions of actors and organizations (i.e. growth machines), all sharing an interest in local growth and its effects on land values, compete with growth machines elsewhere for scarce mobile capital investment, while simultaneously attempting to gain the tacit support of local publics for such urban growth. Following an introductory overview, this entry discusses the urban growth machine in two main parts. The first part sets out the key concepts underlying the growth machine thesis: use value, exchange value and place; place entrepreneurs; growth machines and their allies; competing for mobile capital; and promoting growth as a public good. The second part identifies core issues and debates in relation to the thesis (particularly those made by human geographers), including critiques of: the property focus; the human agency focus; difficulties with international comparison; the conceptualization of local dependency and scale; and the relationship of political projects with local feeling