Publication Type: Conference Paper/Unpublished Manuscript
Review Method: Peer Reviewed
Abstract: Generating functions encode the solution to counting problems in enumerative combinatorics. Among the nicest generating functions are those which can be expressed as a ratio of two polynomials. The coefficients of these "rational generating functions" satisfy a linear constant coefficient recurrence. Permutation patterns are a source of many diverse generating functions in modern enumerative combinatorics. However, it remains a difficult open question to classify which permutation pattern classes lead to rational generating functions. Recent work of the speaker (with H. Denoncourt) has given one construction that transforms permutation pattern classes in a way that preserves rationality of the corresponding generating functions.

In this talk, we present a methodology for developing undergraduate research projects around these ideas based on an REU at UC Davis led by the speaker during Summer 2008. One aspect of the project involves generating sequence data using computer programs. The goal of the project is to seek out new collections of examples of rational permutation pattern classes. Along the way, students learn how to use linear algebra to detect recurrences, and use available tools such as Sloane's Online Encyclopedia of Integer Sequences to compare their enumerative results with those of other researchers.

Publication Type: Conference Paper/Unpublished Manuscript
Review Method: Peer Reviewed
Abstract: The athletic male body has long been idealized in Western civilization, and its dimensions are a key aspect of its iconic status. In this paper, we examine the discourses of the athletic male body as it is presented in the media discourses surrounding the NFL Draft. We focus specifically on the enumerative strategies used to define and delimit the bodies of football draftees. Through a close textual analysis of publications that cover the Draft, we uncover three main themes in the discursive construction of the athletes’ bodies: the delineation of the body in terms of its dimensions; the assessment of the body’s performance; and the body’s productivity in terms of mastery of the sport. In characterizing the athletic body strictly in terms of its relationship to physical space, the discourses invoke aspects of hegemonic masculinity related to size, strength, and the successful use of force. In addition, the deployment of quantification by white team owners and managers in the evaluation of mainly nonwhite players of lower class position, the numeric logics of the Draft reinscribe power hierarchies of race and class.