Bishops and pawns.

The Problem of the Pawns

In this paper we study the number Mm,n of ways to place nonattacking pawns on an m× n chessboard. We find an upper bound for Mm,n and analyse its asymptotic behavior. It turns out that limm,n→∞(Mm,n) 1/mn exists and is bounded from above by (1 + √ 5)/2. Also, we consider a lower bound for Mm,n by reducing this problem to that of tiling an (m + 1)× (n + 1) board with square tiles of size 1×1 and...

Sharing analysis in the Pawns compiler

Pawns is a programming language under development that supports algebraic data types, polymorphism, higher order functions and “pure” declarative programming. It also supports impure imperative features including destructive update of shared data structures via pointers, allowing significantly increased efficiency for some operations. A novelty of Pawns is that all impure “effects” must be made...

Advocacy: bishops press for immigration reform.

Phylogeny and Signal Diversity in Widowbirds and Bishops

Although sexual selection for elaborate signals is well documented in numerous species, the extreme diversity in signal design and expression in many taxa is largely unexplained. This thesis explores phylogenetic, mechanistic and ontogenetic explanations of divergence in two classic condition-dependent signal traits in the African widowbirds and bishops (Euplectes spp.); elongated black tails (...

A q - QUEENS PROBLEM V . THE BISHOPS ’ PERIOD

Part I showed that the number of ways to place q nonattacking queens or similar chess pieces on an n× n square chessboard is a quasipolynomial function of n. We prove the previously empirically observed period of the bishops quasipolynomial, which is exactly 2 for three or more bishops. The proof depends on signed graphs and the Ehrhart theory of inside-out polytopes.