Jane Friedman

More monotonicity theorems for partitions

Consider the collection of all integer partitions whose part sizes lie in a given set. Such a set is called monotone if the generating function has weakly increasing coefficients. The monotone subsets are classified, assuming an open conjecture.

Math Path: Encouraging Female Students in Mathematics through Project-Based Learning.

Abstract Although the number of bachelors degrees in the U.S. awarded to women has gone up, engagement of women in science, technology, engineering, and mathematics (STEM) continues to be low. This paper presents a project-based learning program, informed by education research best practices, designed to provide research experiences to female students early in their academic careers. Mentored by female faculty, students voluntarily collaborate on extracurricular mathematical research projects that they select together based on their interests and passions. They then prepare and share their work at an undergraduate research celebration event at the university and at other conferences.

The conditional Shapley–Shubik measure for ternary voting games

Abstract Ternary voting games (TVGs) model situations where a voter has three options, which can be thought of as yes, no, and abstention. This paper presents ϕ ˜ , an extension of the Shapley–Shubik power measure to ternary voting games. ϕ ˜ measures a voters power as the probability that the voter will be pivotal given that they do not abstain. This contrasts with other extensions of the Shapley–Shubik measure to TVGs, which measure power as the probability that a players vote is pivotal no matter what that vote is. Desirable properties of power measures in SVGs are extended to TVGs and ϕ ˜ is shown to satisfy these properties.

Innovative faculty cohort hire at the university of San Diego

The University of San Diego (USD)s NSF ADVANCE grant, AFFIRM (Advancement of Female Faculty: Institutional climate, Recruitment and Mentoring), focuses on addressing issues related to race and gender for faculty in Science, Technology, Engineering, and Mathematics (STEM). Although a majority of undergraduate students majoring in most STEM disciplines at USD are female, there are not nearly that many women faculty. As part of the grant proposal, the AFFIRM team was promised two new faculty positions by the Provost. In Fall 2013, the team met with the Dean of the College of Arts and Sciences and the Dean of the School of Engineering and the idea of hiring a faculty cohort to facilitate mentoring, diversity, and interdisciplinarity emerged and was approved. Over 200 candidates from diverse backgrounds applied. The candidates that came for on-campus interviews were so impressive that the Provost and Deans agreed to additional hiring opportunities, leading to a cohort of eight female faculty in the STEM fields including four women of color. In this work-in-progress, we discuss our innovative cohort hiring process, and share feedback from members of the cohort, and lessons learned. This innovative process could serve as a model for other campuses.

A Generalization of Odlyzko's Conjecture: the Coefficients of (1 - q) j / ((1 - q 2n ) ⋯(1 - q 2n+2j )) Alternate in Sign

A positivity result is proved that generalizes a conjecture of Odlyzko, previously proved by Stanton and Zeilberger