BONUS ind a bijection between rook placements (problem 4) and partitions of a set (slides Feb 10) which explains the relationship you found in problem 4d. 4. For 0 S k S n, let r(n, k) be the number of ways to place k rooks on a size n triangular checker board. Explanation: a triangular checker board has rows of n, n 1 2,1 squares, so it is a checker board cut along the squares on the diagonal. Rooks must be placed so that no two rooks occupy the same row or the same column. Below is a picture indicating all placements of 2 rooks on a size 3 triangular checker board, showing that r 3, 2-7. BONUS ind a bijection between rook placements (problem 4) and partitions of a set (slides Feb 10) which explains the relationship you found in problem 4d. 4. For 0 S k S n, let r(n, k) be the number of ways to place k rooks on a size n triangular checker board. Explanation: a triangular checker board has rows of n, n 1 2,1 squares, so it is a checker board cut along the squares on the diagonal. Rooks must be placed so that no two rooks occupy the same row or the same column. Below is a picture indicating all placements of 2 rooks on a size 3 triangular checker board, showing that r 3, 2-7