Community-university partnerships offer the potential for a number of mutual benefits, yet working with institutions of higher education can pose unique challenges for community participants. To better understand the community perspective, this paper explores community partners’ satisfaction with their involvement in various forms of community-based learning (e.g., service-learning, internships, community-based research). Drawn from a larger, mixed-methods study of community partners across 13 states, the current analysis assesses community agency representatives’ (N = 201) satisfaction with their community-university partnerships in general as well their satisfaction with specific elements of these collaborations. While the findings reflect generally positive levels of satisfaction overall, several areas of concern are identified, including communication with and presence of faculty, commitment and efficacy of students, and partnership equality and recognition of agency contributions. These findings provide a starting point for improving the community partner experience.

In their recent work on the Castelnuovo-Mumford regularity of the matrix Schubert variety, Pechenik, Speyer, and Weigandt introduced a formula for the degree of any Grothendieck polynomial. We give a new proof of this formula in the special case of vexillary permutations and characterize the set of bumpless pipe dreams which contribute maximal degree terms to the Grothendieck polynomial in this case. We also conjecture a generalization of this characterization to bumpless pipe dreams for non-vexillary permutations. Furthermore, we use bumpless pipe dreams to prove new results about the support of vexillary Grothendieck polynomials, addressing special cases of conjectures of Mészáros, Setiabrata, and St. Dizier.

The central question of knot theory is that of distinguishing links up to isotopy. The first polynomial invariant of links devised to help answer this question was the Alexander polynomial (1928). Almost a century after its introduction, it still presents us with tantalizing questions such as Fox's conjecture (1962) that the absolute values of the coefficients of the Alexander polynomial ∆ L (t) of an alternating link L are unimodal. Fox's conjecture remains open in general, with special cases settled by Hartley (1979) for two-bridged knots, by Murasugi (1985) for a family of alternating algebraic links, and by Ozsváth and Szabó (2003) for the case of genus 2 alternating knots, among others.We settle Fox's conjecture for special alternating links. We do so by proving that a certain multivariate generalization of the Alexander polynomial of special alternating links is Lorentzian. As a consequence, we obtain that the absolute values of the coefficients of ∆ L (t), where L is a special alternating link, form a log-concave sequence with no internal zeros. In particular, they are unimodal.