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I Don't Play Chess: A Study Of Chess Piece Generating Polynomials, Stephen R. Skoch Jan 2015

I Don't Play Chess: A Study Of Chess Piece Generating Polynomials, Stephen R. Skoch

Senior Independent Study Theses

This independent study examines counting problems of non-attacking rook, and non-attacking bishop placements. We examine boards for rook and bishop placement with restricted positions and varied dimensions. In this investigation, we discuss the general formula of a generating function for unrestricted, square bishop boards that relies on the Stirling numbers of the second kind. We discuss the maximum number of bishops we can place on a rectangular board, as well as a brief investigation of non-attacking rook placements on three-dimensional boards, drawing a connection to latin squares.


Beyond Ss: An Analysis Of Alternative Risk Measures, Jai Kedia Jan 2015

Beyond Ss: An Analysis Of Alternative Risk Measures, Jai Kedia

Senior Independent Study Theses

Investors require a return from investing in stock securities that adequately compensate the investors for the risk level assumed. Therefore, any calculation of expected returns from a stock requires knowledge of the risk of the security. While there is no strong consensus on an ideal risk measure, traditionally risk has been conceptualized as volatility and is measured by the ß of the stock or portfolio. This paper hypothesizes that alternative risk measures such as higher order moments, size, leverage, and price-to-book value add explanatory power to the ß when predicting stock returns. Empirical analysis is conducted using both regression and …