Results and conjectures on simultaneous core partitions

An n-core partition is an integer partition whose Young diagram contains no hook lengths equal to n. We consider partitions that are simultaneously a-core and b-core for two relatively prime integers a and b. These are related to abacus diagrams and the combinatorics of the affine symmetric group (type A). We observe that self-conjugate simultaneous core partitions correspond to the combinatorics of type C, and use abacus diagrams to unite the discussion of these two sets of objects. In particular, we prove that (2n)- and (2mn+1)-core partitions correspond naturally to dominant alcoves in the m-Shi arrangement of type C_n, generalizing a result of Fishel--Vazirani for type A. We also introduce a major statistic on simultaneous n- and (n+1)-core partitions and on self-conjugate simultaneous (2n)- and (2n+1)-core partitions that yield q-analogues of the Coxeter-Catalan numbers of type A and type C. We present related conjectures and open questions on the average size of a simultaneous core partition, q-analogs of generalized Catalan numbers, and generalizations to other Coxeter groups. We also discuss connections with the cyclic sieving phenomenon and q,t-Catalan numbers.Comment: 17 pages; to appear in the European Journal of Combinatoric

Stock Options and Chief Executive Compensation

Although stock options are commonly observed in chief executive officer (CEO) com- pensation contracts, there is theoretical controversy about whether stock options are part of the optimal contract. Using a sample of Fortune 500 companies, we solve an agency model calibrated to the company-specifc data and we find that stock options are almost always part of the optimal contract. This result is robust to alternative assumptions about the level of CEO risk-aversion and the disutility associated with their effort. In a supplementary analysis, we solve for the optimal contract when there are no restrictions on the contract space. We find that the optimal contract (which is characterized as a state-contingent payoff to the CEO) typically has option-like features over the most probable range of outcomes.Stock Options, Incentives, Agency Model

Electroproduction of the S(11)meson(1535) resonance at high momentum transfer

The amplitude of the S\sb{11}(1535) resonance at values of four-momentum transfer Q\sp2 \u3e 0 is not explained by the nonrelativistic constituent quark model, and is currently a topic of theoretical interest; in addition, the large branching fraction of this resonance to the proton-$\eta$ decay channel is not well understood. There is also controversy concerning the Q\sp2 regime in which perturbative QCD becomes important in describing nucleon resonances such as the S\sb{11}. The p(e, e\sp\prime p)\eta reaction is an excellent system in which to study this resonance and address the issue of possible perturbative effects: the $p\eta$ channel is not accessible to the $\Delta$ (isospin-$3\over2$) resonances and couples only weakly to N* (isospin-$1\over2$) resonances other than the S\sb{11}(1535). The differential cross section for the process p(e, e\sp\prime p)\eta was measured in Hall C of the Thomas Jefferson National Accelerator Facility (TJNAF) in experiment E94-14 in December 1996. The angular distribution at center-of-momentum energies near the S\sb{11}(1535) was measured for Q\sp2\approx 2.4 and 3.6 GeV\sp2/c\sp2 (the latter being the highest-Q\sp2 exclusive measurement of this process to date). The Short Orbit Spectrometer (SOS) was used to detect recoil electrons and the High Momentum Spectrometer (HMS) was used to detect outgoing protons, with the $\eta$ identified via missing mass. Results of fits to the differential cross section and an extraction of the helicity amplitude A\sbsp{1/2}{p} are presented. The cross section obtained from these new data is about 30% lower than that of the only other high-Q\sp2 exclusive measurement of this process. Comparison with a recent analysis of inclusive (e, e\sp\prime) data provides a lower bound on the S\sb{11}(1535)\to p\eta branching fraction of b\sb{\eta} = 0.45

Graduation Rates of Pell Grant Recipients at Mississippi Community Colleges

The purpose of this study was to determine the effect receiving a Pell Grant or not receiving a Pell Grant had on graduation rates at Mississippi community colleges. National averages suggest that Pell Grant recipients graduate at a much lower rate than non-recipients. This proved not to be the case in Mississippi. There were three Mississippi community colleges that participated in this study. The total number of students involved in the study was 3,479. The colleges provided the researcher information on Pell Grant status, gender, and ethnicity (i.e., Caucasian, African American, Hispanic or non-Hispanic, American Indian, Asian, or other). Students were compared based on their Pell Grant status and then combined with their gender and ethnicity as well as the region of the state in which they attended community college. The researcher used a quasi-experimental design for the study. The data gathered allowed for chi-square tests to be performed based on Pell Grant status, gender, and ethnicity. Each test included all 3,479 students involved in the study. The study used an ANOVA to study the effects Pell Grant status had on graduation rates in the different regions of the state. The study found that the differences among graduation rates for Pell Grant recipients and non-recipients are significant for gender and the different regions of the state. The results are not significant for Pell Grant recipients and non-recipients nor are they significant for Pell Grant recipients and non-recipients combined with ethnicity. Mississippi African Americans and Caucasian students graduate at a much higher rate than the national average. This study finds that Mississippi students perform better than the national average when it comes to graduation rates. Considerations for future research are discussed

Abnormal Accruals in Newly Public Companies: Opportunistic Misreporting or Economic Activity?

Newly public companies tend to exhibit abnormally high accruals in the year of their initial public offering (IPO). Although the prevailing view in the literature is that these accruals are caused by opportunistic misreporting, we show that these accruals do not appear to benefit managers and instead result from the normal economic activity of newly public companies. In particular, and in contrast to the notion that managers benefit from inflating accruals through an inflated issue price, inflated post-IPO equity values, and increased insider trading profits, we find no evidence of a relation between abnormal accruals and these outcomes. Instead, consistent with these accruals resulting from normal economic activity, we find that these accruals are attributable to the investment of IPO proceeds in working capital and that controlling for the amount of IPO proceeds invested in working capital produces a more powerful accrual-based measure of misreporting