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    Critical sets in the elementary abelian 2- and 3- groups

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    In 1998, Khodkar showed that the minimal critical set in the Latin square corresponding to the elementary abelian 2-group of order 16 is of size at most 124. Since the paper was published, improved methods for solving integer programming problems have been developed. Here we give an example of a critical set of size 121 in this Latin square, found through such methods. We also give a new upper bound on the size of critical sets of minimal size for the elementary abelian 2-group of order 2n2^n: 4n3n+42n2n24^{n}-3^{n}+4-2^{n}-2^{n-2}. We speculate about possible lower bounds for this value, given some other results for the elementary abelian 2-groups of orders 32 and 64. An example of a critical set of size 29 in the Latin square corresponding to the elementary abelian 3-group of order 9 is given, and it is shown that any such critical set must be of size at least 24, improving the bound of 21 given by Donovan, Cooper, Nott and Seberry.Comment: 9 page

    Household reports of energy assistance receipt increased 48 percent during recession: Proposed cuts threaten vulnerable families

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    This brief examines heating assistance usage and the implications of President Obama\u27s 2012 budget proposal to cut 2.5billionfromthe2.5 billion from the 5.1 billion energy assistance fund for low-income families at a time when families are struggling with higher energy costs amid a difficult economy. The federal Low-Income Home Energy Assistance Program (LIHEAP) assists vulnerable families in paying their home heating and cooling bills. Nationwide, from the winter of 2006/2007 to the winter of 2009/2010, there was a 48 percent increase in households receiving energy assistance. This growth appears to have accelerated with the recession, particularly in the rural Northeast and Midwest. Many more families are eligible than receive assistance. Brief author Jessica Bean discusses how proposed cuts would have a concrete and immediate impact on families, particularly those in rural areas and in harsh winter climates

    Reliance on supplemental nutrition assistance program continued to rise post-recession

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    This brief uses data from the 2007, 2009, and 2010 American Community Survey to provide an up-to-date look at changes in SNAP receipt over the course of the recession

    Rural and central city residents with multiple children likely to be hardest hit by proposed WIC cuts

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    This brief uses data from the 2007 and 2010 Current Population Survey’s Annual Social and Economic Supplement to describe the distribution of the Special Supplemental Nutrition Program for Women, Infants, and Children (WIC) receipt across the population and to detail place-based differences in receipt. WIC is a nutrition program that serves pregnant or postpartum women, infants, and children up to age 5 (who meet certain criteria) by providing them with nutrition education and checks or vouchers for food purchases. The proposed fiscal year 2012 funding is $733 million less for WIC than fiscal year 2011 levels, and far less than what is needed to serve all who are eligible. This brief describes the implications of the cuts to the WIC budget to help policymakers and service providers to better understand the population likely affected by cuts to WIC funding
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