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A partial formula is provided to calculate the smallest number of vertices possible in a quadrangulation on the closed orientable 2-manifold of given genus. This extends the previously known partial formula due to N. Hartsfield and G. Ringel [J. Comb. Theory, Ser. B, 1989, 46, 84-95]., Comment: 5 pages. arXiv admin note: text overlap with arXiv:1207.1882

We examine the consequences of underreporting of transfer programs in household survey data for several prototypical analyses of low-income populations. We focus on the Current Population Survey (CPS), the source of official poverty and inequality statistics, but provide evidence that our qualitative conclusions are likely to apply to other surveys. We link administrative data for food stamps, TANF, General Assistance, and subsidized housing from New York State to the CPS at the individual level. Program receipt in the CPS is missed for over one-third of housing assistance recipients, 40 percent of food stamp recipients and 60 percent of TANF and General Assistance recipients. Dollars of benefits are also undercounted for reporting recipients, particularly for TANF, General Assistance and housing assistance. We find that the survey data sharply understate the income of poor households, as conjectured in past work by one of the authors. Underreporting in the survey data also greatly understates the effects of anti-poverty programs and changes our understanding of program targeting, often making it seem that welfare programs are less targeted to both the very poorest and middle income households than they are. Using the combined data rather than survey data alone, the poverty reducing effect of all programs together is nearly doubled while the effect of housing assistance is tripled. We also re-examine the coverage of the safety net, specifically the share of people without work or program receipt. Using the administrative measures of program receipt rather than the survey ones often reduces the share of single mothers falling through the safety net by one-half or more. [ABSTRACT FROM AUTHOR]