Publication Type: Conference Paper/Unpublished Manuscript
Review Method: Peer Reviewed
Abstract: The permanent of a matrix is computed similarly to the determinant of a matrix, except that instead of summing over the permutations and alternating signs we make no sign change when computing the permanent. Permanents have myriad applications in combinatorics and graph theory; one particular combinatorial application involves the number of ways to choose a system of distinct representatives from a collection of sets. When working recently with a student on her senior project (related to Sudoku), we searched the literature to find a good bound for the permanent of a $\$(0,1)\$$-matrix. One such bound had a published proof that was complicated and algebraic; we present here a short combinatorial proof and a slight improvement of the bound. We will also look at some numerical results suggesting that for certain matrices this is a very good bound relative to other more general bounds on the permanent. Along the way, we tell a story about the joys of working with students and the delightful understanding possible in combinatorial proofs. We also mention some open questions and some possibilities for undergraduate research.

Publication Type: Conference Paper/Unpublished Manuscript
Abstract: This presentation will focus on data obtained from the National Violent Death Reporting System (NVDRS) that was used to illuminate the circumstances related to homicide among children aged 4 years or less, and to identify demographic groups which may be at increased risk. Standard statistical tests were conducted to determine homicide rates among children aged 4 years or less, and to investigate infant/child homicide rates by race, gender, and other relevant circumstances. We fit a Poisson regression model to the sample data to investigate the multivariate relationship between infant/child homicide and available demographic information. Our findings indicate that Whites were 0.29 times as likely to be victims as African Americans, and females were 0.86 times as likely as males. Perpetrators were commonly parents / caregivers. The majority of infant / child homicides occurred in houses or apartments, using weapons of opportunity. In order to reduce infant/child homicide, intervention strategies should target the home environment and attend to ways by which to enhance parenting skills and the ability to cope with the stressors associated with child rearing.