Combinatorial Formulas for Macdonald and Hall-Littlewood Polynomials of Types A and C. Extended Abstract

A breakthrough in the theory of (type A) Macdonald polynomials is due to Haglund, Haiman and Loehr, who exhibited a combinatorial formula for these polynomials in terms of fillings of Young diagrams. Recently, Ram and Yip gave a formula for the Macdonald polynomials of arbitrary type in terms of the corresponding affine Weyl group. In this paper, we show that a Haglund-Haiman-Loehr type formula follows naturally from the more general Ram-Yip formula, via compression. Then we extend this approach to the Hall-Littlewood polynomials of type C, which are specializations of the corresponding Macdonald polynomials at q=0. We note that no analog of the Haglund-Haiman-Loehr formula exists beyond type A, so our work is a first step towards finding such a formula

Relationship Between Scholastic and Health Behaviors and Reading Level in Adolescent Females

This was a study of 102 adolescent females, 12-20 years of age, presenting to a central city clinic for medical care. Participants completed an oral questionnaire that included demographics, and questions regarding scholastic history, sexual behavior, and substance use. Each subject completed the Accuracy Level Test (ALT), a reading test. The subject\u27s reading test grade level was subtracted from her appropriate grade in school to give a reading delay level (RDL). The mean reading grade level for all subjects was 6.7 ±2.6 and the average reading delay was 4.5 ±2.5 grades. Poor school attenders had greater reading delays (5.8 ±3.4 grades behind vs. 4.3 ±2.2 for good attenders

Type C parking functions and a zeta map

We introduce type C parking functions, encoded as vertically labelled lattice paths and endowed with a statistic dinv'. We define a bijection from type C parking functions to regions of the Shi arrangement of type C, encoded as diagonally labelled ballot paths and endowed with a natural statistic area'. This bijection is a natural analogue of the zeta map of Haglund and Loehr and maps dinv' to area'. We give three different descriptions of it.Comment: 12 page

Finiteness properties of cubulated groups

We give a generalized and self-contained account of Haglund-Paulin's wallspaces and Sageev's construction of the CAT(0) cube complex dual to a wallspace. We examine criteria on a wallspace leading to finiteness properties of its dual cube complex. Our discussion is aimed at readers wishing to apply these methods to produce actions of groups on cube complexes and understand their nature. We develop the wallspace ideas in a level of generality that facilitates their application. Our main result describes the structure of dual cube complexes arising from relatively hyperbolic groups. Let H_1,...,H_s be relatively quasiconvex codimension-1 subgroups of a group G that is hyperbolic relative to P_1,...,P_r. We prove that G acts relatively cocompactly on the associated dual CAT(0) cube complex C. This generalizes Sageev's result that C is cocompact when G is hyperbolic. When P_1,...,P_r are abelian, we show that the dual CAT(0) cube complex C has a G-cocompact CAT(0) truncation.Comment: 58 pages, 12 figures. Version 3: Revisions and slightly improved results in Sections 7 and 8. Several theorem numbers have changed from the previous versio

Reducing Sexual Risk with Practice of Periodic Secondary Abstinence

Objective: Test a novel intervention to help sexually experienced girls increase abstinence behaviors and attitudes. Design: A quasi-experimental repeated measures design using qualitative and quantitative data. Setting: Two alternative public schools. Participants: Thirty-three females whose mean age was 16 and who were 79% African American participated. Most (79%) had experienced a pregnancy. Intervention: A 6 session, weekly, interactive intervention was delivered. Data were collected at baseline, last session, and at 5 and 7 month follow-ups. Main Outcome Measures: Measured outcomes related to abstinence included participants’ reasons, behaviors, stages of change, and attitudes. Results: The most common reason for abstinence was not wanting to have sex. At each postintervention data collection point, most participants (greater than or equal to 74%) reported that they had purposefully avoided sex. Duration of consecutive days of abstinence increased although only significantly at 5 month follow-up. Abstinence behaviors increased with the largest change from first to last session. Stage of change advanced from preparation to action by 7 month follow-up. Attitudes toward abstinence became more favorable. Conclusion: Effective sexual risk reduction interventions are critically needed to promote safety. Nurses may assist young women to decrease their sexual risks by teaching them to practice periodic abstinence

Light dynamics in glass-vanadium dioxide nanocomposite waveguides with thermal nonlinearity

We address the propagation of laser beams in Si02-VO2 nanocomposite waveguides with thermo-optical nonlinearity. We show that the large modifications of the absorption coefficient as well as notable changes of refractive index of VO2 nanoparticles embedded into the SiO2 host media that accompany the semiconductor-to-metal phase transition may lead to optical limiting in the near-infrared wave range.Comment: 13 pages, 3 figures, to appear in Optics Letter