Rook Placements and Jordan Forms of Upper-Triangular Nilpotent Matrices

The set of $n$ by $n$ upper-triangular nilpotent matrices with entries in a finite field $\mathbb{F}_q$ has Jordan canonical forms indexed by partitions $\lambda \vdash n$. We present a combinatorial formula for computing the number $F_\lambda(q)$ of matrices of Jordan type $\lambda$ as a weighted sum over standard Young tableaux. We construct a bijection between paths in a modified version of Young's lattice and non-attacking rook placements, which leads to a refinement of the formula for $F_\lambda(q)$.

Economic Effects of Tax Evasion on Jordanian Economy

This study aims to clarify the economic effects of tax evasion especially on the Jordanian economy. The researchers has depended on the literature to highlight the negative effects of tax evasion on the economy of states. And by analyzing some statistics published by the Economic and Social council of Jordan, the results showed the tax evasion in Jordan forms a real problem because it amounted a high rate of revenue. Therefore the government should treat the evaders by more rigor.