Stanley's character polynomials and coloured factorisations in the symmetric group

In Stanley [R.P. Stanley, Irreducible symmetric group characters of rectangular shape, Sém. Lothar. Combin. 50 (2003) B50d, 11 p.] the author introduces polynomials which help evaluate symmetric group characters and conjectures that the coefficients of the polynomials are positive. In [R.P. Stanley, A conjectured combinatorial interpretation of the normalised irreducible character values of the symmetric group, math.CO/0606467, 2006] the same author gives a conjectured combinatorial interpretation for the coefficients of the polynomials. Here, we prove the conjecture for the terms of highest degree

Proof of Stanley's conjecture about irreducible character values of the symmetric group

R. Stanley has found a nice combinatorial formula for characters of irreducible representations of the symmetric group of rectangular shape. Then, he has given a conjectural generalisation for any shape. Here, we will prove this formula using shifted Schur functions and Jucys-Murphy elements.Comment: 9 page

An explicit form for Kerov's character polynomials

Kerov considered the normalized characters of irreducible representations of the symmetric group, evaluated on a cycle, as a polynomial in free cumulants. Biane has proved that this polynomial has integer coefficients, and made various conjectures. Recently, Sniady has proved Biane's conjectured explicit form for the first family of nontrivial terms in this polynomial. In this paper, we give an explicit expression for all terms in Kerov's character polynomials. Our method is through Lagrange inversion.Comment: 17 pages, 1 figur

Perceived Centrality in Social Networks Increases Women’s Expectations of Confronting Sexism

This paper integrates the study of intergroup relations and social network cognition, predicting that women who occupy central (vs. peripheral) advice network positions are more likely to confront a coworker’s gender-biased comment. Study 1 offers correlational evidence of the predicted link between perceived advice network centrality and confronting among employed women, uniquely in advice (but not communication) networks. Study 2 replicates and investigates two possible mechanisms–perceptions of the situation as public and perceived risk of confronting. Study 3 rules out order effects and tests an additional mechanism (expectations of the network members). Study 4 is an experiment that shows people expect central (vs. peripheral) women to confront more, even when she is lower (vs. equal) power. Study 5 replicates the core hypothesis in retrospective accounts of women’s responses to real workplace gender bias. Study 6 compares multiple potential mechanisms to provide greater insight into why centrality reliably predicts confrontation

Tight glycemic control: what do we really know, and what should we expect?

Tight glycemic control has engendered large numbers of investigations, with conflicting results. The world has largely embraced intensive insulin as a practice, but applies this therapy with great variability in the manner of glucose control and measurement. The present commentary reviews what we actually know with certainty from this vast sea of literature, and what we can expect looking forward

What happens after prejudice is confronted in the workplace? How mindsets affect minorities' and women's outlook on future social relations

Organizations are increasingly concerned with fostering successful diversity. Toward this end, diversity research has focused on trying to reduce prejudice and biased behavior. But what happens when prejudice in the workplace inevitably occurs? Research also needs to focus on whether recovery and repair of social relations after incidents of prejudice are possible. To begin investigating this question, we develop a new framework for understanding reactions to prejudice in the workplace. We hypothesized that when women and minorities choose to confront a prejudiced comment in a workplace interaction (vs. remain silent) and hold a growth (vs. fixed) mindset — the belief that others can change — they remain more positive in their subsequent outlook in the workplace. Studies 1a, 1b, and 2 used hypothetical workplace scenarios to expose participants to someone who expressed bias; Study 3 ensured real-world relevance by eliciting retrospective accounts of workplace bias from African American employees. Across studies, women and minorities who confronted the perpetrator of prejudice exhibited more positive subsequent expectations of that co-worker when they held a growth mindset. Importantly, these more positive expectations were associated with reports of greater workplace belonging (Study 2), ratings of improved relations with co-workers who had displayed bias (Study 3), and greater workplace satisfaction (Studies 2-3). Thus, a growth mindset contributes to successful workplace diversity by protecting women’s and minorities’ outlook when they opt to confront expressions of bias

Respiratory metabolism in Oreochromis mossambicus, Peters under different environmental conditions

Oxygen consumption in Oreochromis mossambicus, Peters (3-60g in weight) was measured under different stress conditions at a constant temperature of 20±1°C. The rate of oxygen consumption was significantly higher (0.170 ml gˉ¹hˉ¹)at a salinity of 30x10ˉ³ compared with that (0.132ml gˉ¹hˉ¹) in freshwater. The oxygen consumption was also found to be affected by changes in pH. Weight specific rate decreased significantly from 0.113 to 0.045 ml gˉ¹hˉ¹ with increasing body weight. A positive correlation was recorded between availability of dissolved oxygen and the rate of oxygen consumption by the fish. While copper sulphate and malachite green inhibited the respiratory metabolism, formaldehyde treatment raised it from 0.088 to 0.118ml gˉ¹hˉ¹

Identical applicant but different outcomes: the impact of gender versus race salience in hiring

People belong to multiple social groups, which may have conflicting stereotypic associations. A manager evaluating an Asian woman for a computer programming job could be influenced by negative gender stereotypes or by positive racial stereotypes. We hypothesized that evaluations of job candidates can depend upon what social group is more salient, even when both are apparent. In three studies, using student (Study 1) and non-student (Studies 2 and 3) samples, we compared ratings of an Asian-American female applicant, after subtly making her race or gender salient in stereotypically male employment contexts. Consistent with our predictions, we found evidence that men rated her as more skilled (Studies 1 and 3), more hirable (Studies 1-3), and offered her more pay (Study 2) in science and technology-related positions when her race, rather than gender, was salient. The theoretical implications for person perception and practical implications in employment contexts are discussed

Whites' perceptions of biracial individuals' race shift when biracials speak out against bias

Previous research suggests that a person’s racial identity shapes the way others respond when that person speaks out against racial prejudice. In the present research, we consider instead how speaking out against racial prejudice shapes people’s impressions of a confronter’s racial identity, such as experiences with discrimination, stereotype enactment, and even phenotype. Two experiments found that White perceivers evaluated a Black/White biracial person who spoke out against (versus remained silent to) racial prejudice as more stigmatized and Black-identified, and as having more stereotypically Black (vs. White) preferences and Black (vs. White) ancestry when they confronted. The faces of biracial confronters (vs. non-confronters) were also recalled as more phenotypically Black (vs. White; Study 2). This evidence suggests that speaking out against bias colors Whites’ impressions of a biracial target across both subjective and objective measures of racial identity. Implications for interracial interactions and interpersonal perception are discussed

Is education a fundamental right? People's lay theories about intellectual potential drive their positions on education

Does every child have a fundamental right to receive a high quality education? We propose that people’s beliefs about whether “nearly everyone” or “only some people” have high intellectual potential drive their positions on education. Three studies found that the more people believed that nearly everyone has high potential, the more they viewed education as a fundamental human right. Further, people who viewed education as a fundamental right, in turn, (1) were more likely to support the institution of free public education; (2) were more concerned upon learning that students in the country were not performing well academically compared to students in peer nations; and (3) were more likely to support redistributing educational funds more equitably across wealthier and poorer school districts. The studies show that people’s beliefs about intellectual potential can influence their positions on education, which can affect the future quality of life for countless students