A Property of the Roots of r-D Rook Polynomials

作者：Aristidou Michael^*

来源：Ars Combinatoria, 2010, 96: 331-341.

• rook polynomial
• sum of roots
• algorithm
• rook matrix

In this paper, we prove an interesting property of rook polynomials for 2-D square boards and extend that for rook polynomials for 3-D cubic, and r-D "hypercubic", boards. In particularly, we prove that for r-D rook polynomials the modulus of the sum of their roots equals their degree. We end with some further questions, mainly for the 2-D and 3-D case, that could serve as future projects.

• 出版日期2010-7