The set of autotopisms of partial Latin squares

Symmetries of a partial Latin square are determined by its autotopism group. Analogously to the case of Latin squares, given an isotopism $\Theta$, the cardinality of the set $\mathcal{PLS}_{\Theta}$ of partial Latin squares which are invariant under $\Theta$ only depends on the conjugacy class of the latter, or, equivalently, on its cycle structure. In the current paper, the cycle structures of the set of autotopisms of partial Latin squares are characterized and several related properties studied. It is also seen that the cycle structure of $\Theta$ determines the possible sizes of the elements of $\mathcal{PLS}_{\Theta}$ and the number of those partial Latin squares of this set with a given size. Finally, it is generalized the traditional notion of partial Latin square completable to a Latin square.Comment: 20 pages, 4 table

Correlates of Poverty and Participation in Food Assistance Programs among Hispanic Elders in Massachusetts

Hispanics are a rapidly growing population in Massachusetts, but little is known about the health, nutrition, and economic situation of the elder segment of these groups. In this report, we examine factors associated with poverty and the use of food assistance programs, using data from an NIA-funded project on Hispanic elders in Massachusetts. Poverty is shown to be a major problem with differences across Hispanic subgroups. Puerto Rican and Dominican elders have lower incomes, on average, than other Hispanics—mainly Cubans, and Central and South Americans—or than non-Hispanic whites living in the same neighborhoods. Older age, lower education, and living alone are associated with poverty within this population. Limited income sources and recent immigration are also important factors. Hispanic elders are more likely to receive SSI benefits, but are much less likely to have pension income. Financial insecurity in old age among Hispanics is associated with more chronic ailment and mobility limitations. Puerto Rican and Dominican elders have the highest poverty and disability rates and report the most food insecurity. However, with the exception of the Food Stamp program, participation in food programs tends to be very low for these Hispanic elders. Given the prevalence of problems demonstrated by these groups, more attention to program outreach and adaptation for Hispanic elders is needed.