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A rook polynomial is a polynomial R_(m,n)(x)=sum_(k=0)^(min(m,n))r_kx^k (1) whose number of ways k nonattacking rooks can be arranged on an m×n chessboard. The rook ...

Let one grain of wheat be placed on the first square of a chessboard, two on the second, four on the third, eight on the fourth, etc. How many grains total are placed on an ...

The Thue-Morse sequence, also called the Morse-Thue sequence or Prouhet-Thue-Morse sequence (Allouche and Cosnard 2000), is one of a number of related sequences of numbers ...

A square which can be dissected into a number of smaller squares with no two equal is called a perfect square dissection (or a squared square). Square dissections in which ...

The m×n king graph is a graph with mn vertices in which each vertex represents a square in an m×n chessboard, and each edge corresponds to a legal move by a king. The number ...

A game is defined as a conflict involving gains and losses between two or more opponents who follow formal rules. The study of games belongs to a branch of mathematics known ...

The triangular grid graph T_n is the lattice graph obtained by interpreting the order-(n+1) triangular grid as a graph, with the intersection of grid lines being the vertices ...

Checkers is a two-player game with the most common variant played on an 8×8 checkerboard with each player starts with twelve pieces of a fixed color on opposite sites of the ...

If ABB^' and AC^'C are straight lines with BC and B^'C^' intersecting at D and AB+BD=AC^'+C^'D, then AB^'+B^'D=AC+CD. The origin and some history of this theorem are ...

Let L=(L, ^ , v ) and K=(K, ^ , v ) be lattices, and let h:L->K. If h is one-to-one and is a join-homomorphism, then it is a join-embedding.