Bishop's vision

Advocacy: bishops press for immigration reform.

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.

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 IV. QUEENS, BISHOPS, NIGHTRIDERS (AND ROOKS)

Parts I–III showed that the number of ways to place q nonattacking queens or similar chess pieces on an n × n chessboard is a quasipolynomial function of n whose coefficients are essentially polynomials in q and, for pieces with some of the queen’s moves, proved formulas for these counting quasipolynomials for small numbers of pieces and highorder coefficients of the general counting quasipolyn...

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.