バシク行列の解析

バシク行列の解析

\begin{array}{ll} \Psi_\Omega(0)&=&(0)\\ \Psi_\Omega(1)&=&(0)(1)\\ \Psi_\Omega(n)&=&(0)(1)\cdot n\\ \Psi_\Omega(\Psi_\Omega(\Omega))&=&(0,0)(1,1)\\ \Psi_\Omega(\Omega\cdot n)&=&(n,n)\\ \Psi_\Omega(\phi_0(\Omega+1))&=&(1,1,1)\\ \Psi_\Omega(\phi_0(\Omega+n))&=&(1,1,1)(2,2,1)\cdot n\\ \Psi_\Omega(\phi_0(\Omega+\Psi_\Omega(\phi_0(\Omega\cdot2))))&=&(1,1,1)(2,2,1)(3,2,0)\\ \Psi_\Omega(\phi_0(\Omega+\Psi_\Omega(\phi_0(\Omega\cdot2))+n))&=&(1,1,1)(2,2,1)(3,2,0)(2,2,1)\cdot n\\ \Psi_\Omega(\phi_0(\Omega+\Psi_\Omega(\phi_0(\Omega\cdot2+1)))&=&(1,1,1)(2,2,1)(3,2,1)\\ \Psi_\Omega(\phi_0(\Omega+\Psi_\Omega(\phi_0(\Omega\cdot2+n)))&=&(1,1,1)(2,2,1)(3,3,1)\cdot n\\ \Psi_\Omega(\phi_0(\Omega+\Psi_\Omega(\phi_0(\Omega\cdot2+\Psi_\Omega(\phi_0(\Omega\cdot3))))&=&(1,1,1)(2,2,1)(3,3,1)(4,3,0)\\ \Psi_\Omega(\phi_0(\phi_0(\Omega+1)))&=&(1,1,1)(2,2,2)\\ \Psi_\Omega(\phi_1(\Omega+1))&=&(1,1,1,1)\\ \Psi_\Omega(\phi_1(\Omega+2))&=&(1,1,1,1,1)\\ \Psi_\Omega(\Psi_\Omega(\phi_1(\Omega+\omega)))&=&Bashicu\ matrix\\ \Psi_\Omega(\Psi_\Omega(\phi_2(\Omega+1)))&=&Bashicu\ sequence\\ \end{array}