BMS分析Part1：0~BO

本条目展示BMS强度分析的第一部分

$\varnothing =0$

$(0)=1$

$(0)(0)=2$

$(0)(0)(0)=3$

$(0)(1)=(0)(0)(0)(0)(0)...=\omega$

$(0)(1)(0)=\omega +1$

$(0)(1)(0)(0)=\omega +2$

$(0)(1)(0)(1)=\omega \times 2$

$(0)(1)(0)(1)(0)(1)=\omega \times 3$

$(0)(1)(1)=(0)(1)(0)(1)(0)(1)...={\omega }^2$

$(0)(1)(1)(0)={\omega }^2+1$

$(0)(1)(1)(0)(1)={\omega }^2+\omega$

$(0)(1)(1)(0)(1)(0)(1)={\omega }^2+\omega \times 2$

$(0)(1)(1)(0)(1)(1)={\omega }^2\times 2$

$(0)(1)(1)(0)(1)(1)(0)(1)={\omega }^2\times 2+\omega$

$(0)(1)(1)(0)(1)(1)(0)(1)(1)={\omega }^2\times 3$

$(0)(1)(1)(1)={\omega }^3$

$(0)(1)(1)(1)(1)={\omega }^4$

$(0)(1)(2)=(0)(1)(1)(1)(1)...={\omega }^{\omega }$

$(0)(1)(2)(0)(1)(2)={\omega }^{\omega }\times 2$

$(0)(1)(2)(1)={\omega }^{\omega +1}$

$(0)(1)(2)(1)(1)={\omega }^{\omega +2}$

$(0)(1)(2)(1)(1)(1)={\omega }^{\omega +3}$

$(0)(1)(2)(1)(2)={\omega }^{\omega \times 2}$

$(0)(1)(2)(1)(2)(1)(2)={\omega }^{\omega \times 3}$

$(0)(1)(2)(2)={\omega }^{{\omega }^2}$

$(0)(1)(2)(2)(1)={\omega }^{{\omega }^2+1}$

$(0)(1)(2)(2)(1)(2)={\omega }^{{\omega }^2+\omega }$

$(0)(1)(2)(2)(1)(2)(2)={\omega }^{{\omega }^2\times 2}$

$(0)(1)(2)(2)(1)(2)(2)(1)(2)(2)={\omega }^{{\omega }^2\times 3}$

$(0)(1)(2)(2)(2)={\omega }^{{\omega }^3}$

$(0)(1)(2)(2)(2)(2)={\omega }^{{\omega }^4}$

$(0)(1)(2)(3)=(0)(1)(2)(2)(2)(2)...={\omega }^{{\omega }^{\omega }}$

$(0)(1)(2)(3)(4)={\omega }^{{\omega }^{{\omega }^{\omega }}}$

$(0)(1)(2)(3)(4)(5)={\omega }^{{\omega }^{{\omega }^{{\omega }^{\omega }}}}$

$(0)(1,1)=(0)(1)(2)(3)(4)(5)(6)...={\epsilon }_0$

BMS	Veblen	MOCF
$(0)(1,1)$	${\epsilon }_0$	$\psi (0)$
$(0)(1,1)(0,0)$	${\epsilon }_0+1$
$(0)(1,1)(0,0)(1,0)$	${\epsilon }_0+\omega$
$(0)(1,1)(0,0)(1,1)$	${\epsilon }_0\times 2$
$(0)(1,1)(0,0)(1,1)(0,0)(1,1)$	${\epsilon }_0\times 3$
$(0)(1,1)(1,0)$	${\epsilon }_0\times \omega$
$(0)(1,1)(1,0)(1,0)$	${\epsilon }_0\times {\omega }^2$
$(0)(1,1)(1,0)(2,0)$	${\epsilon }_0\times {\omega }^{\omega }$
$(0)(1,1)(1,0)(2,0)(3,0)$	${\epsilon }_0\times {\omega }^{{\omega }^{\omega }}$
$(0)(1,1)(1,0)(2,1)$	${\epsilon }_0^2$
$(0)(1,1)(1,0)(2,1)(1,0)(2,0)$	${\epsilon }_0^2\times \omega$
$(0)(1,1)(1,0)(2,1)(1,0)(2,0)(3,0)$	${\epsilon }_0^2\times {\omega }^{\omega }$
$(0)(1,1)(1,0)(2,1)(1,0)(2,1)$	${\epsilon }_0^3$
$(0)(1,1)(1,0)(2,1)(1,0)(2,1)(1,0)(2,1)$	${\epsilon }_0^4$
$(0)(1,1)(1,0)(2,1)(2,0)$	${\epsilon }_0^{\omega }$
$(0)(1,1)(1,0)(2,1)(2,0)(1,0)(2,1)$	${\epsilon }_0^{\omega +1}$
$(0)(1,1)(1,0)(2,1)(2,0)(1,0)(2,1)(1,0)(2,1)$	${\epsilon }_0^{\omega +2}$
$(0)(1,1)(1,0)(2,1)(2,0)(1,0)(2,1)(2,0)$	${\epsilon }_0^{\omega \times 2}$
$(0)(1,1)(1,0)(2,1)(2,0)(1,0)(2,1)(2,0)(1,0)(2,1)(2,0)$	${\epsilon }_0^{\omega \times 3}$
$(0)(1,1)(1,0)(2,1)(2,0)(2,0)$	${\epsilon }_0^{{\omega }^2}$
$(0)(1,1)(1,0)(2,1)(2,0)(3,0)$	${\epsilon }_0^{{\omega }^{\omega }}$
$(0)(1,1)(1,0)(2,1)(2,0)(3,0)(4,0)$	${\epsilon }_0^{{\omega }^{{\omega }^{\omega }}}$
$(0)(1,1)(1,0)(2,1)(2,0)(3,1)$	${\epsilon }_0^{{\epsilon }_0}$
$(0)(1,1)(1,0)(2,1)(2,0)(3,1)(3,0)(4,1)$	${\epsilon }_0^{{\epsilon }_0^{{\epsilon }_0}}$
$(0)(1,1)(1,0)(2,1)(2,0)(3,1)(3,0)(4,1)(4,0)(5,1)$	${\epsilon }_0^{{\epsilon }_0^{{\epsilon }_0^{{\epsilon }_0}}}$
$(0)(1,1)(1,1)$	${\epsilon }_1$	$\psi (1)$
$(0)(1,1)(1,1)(0,0)(1,1)(1,1)$	${\epsilon }_1\times 2$
$(0)(1,1)(1,1)(1,0)$	${\epsilon }_1\times \omega$
$(0)(1,1)(1,1)(1,0)(2,1)$	${\epsilon }_1\times {\epsilon }_0$
$(0)(1,1)(1,1)(1,0)(2,1)(2,0)(3,1)$	${\epsilon }_1\times {\epsilon }_0^2$
$(0)(1,1)(1,1)(1,0)(2,1)(2,0)(3,1)(3,0)(4,1)$	${\epsilon }_1\times {\epsilon }_0^{{\epsilon }_0}$
$(0)(1,1)(1,1)(1,0)(2,1)(2,1)$	${\epsilon }_1^2$
$(0)(1,1)(1,1)(1,0)(2,1)(2,1)(2,0)$	${\epsilon }_1^{\omega }$
$(0)(1,1)(1,1)(1,0)(2,1)(2,1)(2,0)(3,1)$	${\epsilon }_1^{{\epsilon }_0}$
$(0)(1,1)(1,1)(1,0)(2,1)(2,1)(2,0)(3,1)(3,1)$	${\epsilon }_1^{{\epsilon }_1}$
$(0)(1,1)(1,1)(1,0)(2,1)(2,1)(2,0)(3,1)(3,1)(3,0)(4,1)(4,1)$	${\epsilon }_1^{{\epsilon }_1^{{\epsilon }_1}}$
$(0)(1,1)(1,1)(1,1)$	${\epsilon }_2$	$\psi (2)$
$(0)(1,1)(1,1)(1,1)(1,1)$	${\epsilon }_3$	$\psi (3)$
$(0)(1,1)(2,0)$	${\epsilon }_{\omega }$	$\psi (\omega )$
$(0)(1,1)(2,0)(1,0)$	${\epsilon }_{\omega }\times \omega$
$(0)(1,1)(2,0)(1,0)(2,1)$	${\epsilon }_{\omega }\times {\epsilon }_0$
$(0)(1,1)(2,0)(1,0)(2,1)(2,1)$	${\epsilon }_{\omega }\times {\epsilon }_1$
$(0)(1,1)(2,0)(1,0)(2,1)(2,1)(2,1)$	${\epsilon }_{\omega }\times {\epsilon }_2$
$(0)(1,1)(2,0)(1,0)(2,1)(2,1)(2,1)(2,1)$	${\epsilon }_{\omega }\times {\epsilon }_3$
$(0)(1,1)(2,0)(1,0)(2,1)(3,0)$	${\epsilon }_{\omega }^2$
$(0)(1,1)(2,0)(1,0)(2,1)(3,0)(2,0)(3,1)(4,0)$	${\epsilon }_{\omega }^{{\epsilon }_{\omega }}$
$(0)(1,1)(2,0)(1,1)$	${\epsilon }_{\omega +1}$	$\psi (\omega +1)$
$(0)(1,1)(2,0)(1,1)(1,1)$	${\epsilon }_{\omega +2}$	$\psi (\omega +2)$
$(0)(1,1)(2,0)(1,1)(1,1)(1,1)$	${\epsilon }_{\omega +3}$	$\psi (\omega +3)$
$(0)(1,1)(2,0)(1,1)(2,0)$	${\epsilon }_{\omega \times 2}$	$\psi (\omega \times 2)$
$(0)(1,1)(2,0)(1,1)(2,0)(1,1)(2,0)$	${\epsilon }_{\omega \times 3}$	$\psi (\omega \times 3)$
$(0)(1,1)(2,0)(2,0)$	${\epsilon }_{{\omega }^2}$	$\psi ({\omega }^2)$
$(0)(1,1)(2,0)(2,0)(2,0)$	${\epsilon }_{{\omega }^3}$	$\psi ({\omega }^3)$
$(0)(1,1)(2,0)(3,0)$	${\epsilon }_{{\omega }^{\omega }}$	$\psi ({\omega }^{\omega })$
$(0)(1,1)(2,0)(3,0)(4,0)$	${\epsilon }_{{\omega }^{{\omega }^{\omega }}}$	$\psi ({\omega }^{{\omega }^{\omega }})$
$(0)(1,1)(2,0)(3,1)$	${\epsilon }_{{\epsilon }_0}$	$\psi (\psi (0))$
$(0)(1,1)(2,0)(3,1)(1,1)$	${\epsilon }_{{\epsilon }_0+1}$	$\psi (\psi (0)+1)$
$(0)(1,1)(2,0)(3,1)(3,1)$	${\epsilon }_{{\epsilon }_1}$	$\psi (\psi (1))$
$(0)(1,1)(2,0)(3,1)(4,0)$	${\epsilon }_{{\epsilon }_{\omega }}$	$\psi (\psi (\omega ))$
$(0)(1,1)(2,0)(3,1)(4,0)(5,1)$	${\epsilon }_{{\epsilon }_{{\epsilon }_0}}$	$\psi (\psi (\psi (0)))$
$(0)(1,1)(2,0)(3,1)(4,0)(5,1)(6,0)(7,1)$	${\epsilon }_{{\epsilon }_{{\epsilon }_{{\epsilon }_0}}}$	$\psi (\psi (\psi (\psi (0))))$
$(0)(1,1)(2,1)$	${\zeta }_0$	$\psi (\mathrm{\Omega })$
$(0)(1,1)(2,1)(1,0)(2,1)(3,1)$	${\zeta }_0^2$
$(0)(1,1)(2,1)(1,0)(2,1)(3,1)(2,0)(3,1)(4,1)$	${\zeta }_0^{{\zeta }_0}$
$(0)(1,1)(2,1)(1,1)$	${\epsilon }_{{\zeta }_0+1}$	$\psi (\mathrm{\Omega }+1)$
$(0)(1,1)(2,1)(1,1)(1,0)(2,1)(3,1)(2,1)$	${\epsilon }_{{\zeta }_0+1}^2$
$(0)(1,1)(2,1)(1,1)(1,1)$	${\epsilon }_{{\zeta }_0+2}$	$\psi (\mathrm{\Omega }+2)$
$(0)(1,1)(2,1)(1,1)(2,0)$	${\epsilon }_{{\zeta }_0+\omega }$	$\psi (\mathrm{\Omega }+\omega )$
$(0)(1,1)(2,1)(1,1)(2,0)(3,1)$	${\epsilon }_{{\zeta }_0+{\epsilon }_0}$	$\psi (\mathrm{\Omega }+\psi (0))$
$(0)(1,1)(2,1)(1,1)(2,0)(3,1)(4,1)$	${\epsilon }_{{\zeta }_0\times 2}$	$\psi (\psi (\mathrm{\Omega })\times 2)$
$(0)(1,1)(2,1)(1,1)(2,0)(3,1)(4,1)(3,1)$	${\epsilon }_{{\epsilon }_{{\zeta }_0+1}}$	$\psi (\psi (\mathrm{\Omega }+1))$
$(0)(1,1)(2,1)(1,1)(2,0)(3,1)(4,1)(3,1)(4,0)(5,1)(6,1)(5,1)$	${\epsilon }_{{\epsilon }_{{\epsilon }_{{\zeta }_0+1}}}$	$\psi (\psi (\psi (\mathrm{\Omega }+1)))$
$(0)(1,1)(2,1)(1,1)(2,1)$	${\zeta }_1$	$\psi (\mathrm{\Omega }\times 2)$
$(0)(1,1)(2,1)(1,1)(2,1)(1,1)$	${\epsilon }_{{\zeta }_1+1}$	$\psi (\psi (\mathrm{\Omega }\times 2+1))$
$(0)(1,1)(2,1)(1,1)(2,0)$	${\epsilon }_{{\zeta }_1+\omega }$	$\psi (\psi (\mathrm{\Omega }\times 2+\omega ))$
$(0)(1,1)(2,1)(1,1)(2,1)(1,1)(2,1)$	${\zeta }_2$	$\psi (\mathrm{\Omega }\times 3)$
$(0)(1,1)(2,1)(1,1)(2,1)(1,1)(2,1)(1,1)(2,1)$	${\zeta }_3$
$(0)(1,1)(2,1)(2,0)$	${\zeta }_{\omega }$
$(0)(1,1)(2,1)(2,0)(2,0)$	${\zeta }_{{\omega }^2}$
$(0)(1,1)(2,1)(2,0)(3,1)$	${\zeta }_{{\epsilon }_0}$
$(0)(1,1)(2,1)(2,0)(3,1)(4,1)$	${\zeta }_{{\zeta }_0}$
$(0)(1,1)(2,1)(2,0)(3,1)(4,1)(4,0)(5,1)(6,1)$	${\zeta }_{{\zeta }_{{\zeta }_0}}$
$(0)(1,1)(2,1)(2,1)$	${\eta }_0$
$(0)(1,1)(2,1)(2,1)(1,1)$	${\epsilon }_{{\eta }_0+1}$
$(0)(1,1)(2,1)(2,1)(1,1)(2,1)$	${\zeta }_{{\eta }_0+1}$
$(0)(1,1)(2,1)(2,1)(1,1)(2,1)(2,0)(3,1)(4,1)(4,1)(3,1)(4,1)$	${\zeta }_{{\zeta }_{{\eta }_0+1}}$
$(0)(1,1)(2,1)(2,1)(1,1)(2,1)(2,1)$	${\eta }_1$
$(0)(1,1)(2,1)(2,1)(1,1)(2,1)(2,1)(1,1)(2,1)(2,1)$	${\eta }_2$
$(0)(1,1)(2,1)(2,1)(2,0)$	${\eta }_{\omega }$
$(0)(1,1)(2,1)(2,1)(2,1)$	$\phi (4,0)$	$\psi ({\mathrm{\Omega }}^3)$
$(0)(1,1)(2,1)(3,0)$	$\phi (\omega ,0)$	$\psi ({\mathrm{\Omega }}^{\omega })$
$(0)(1,1)(2,1)(3,0)(1,1)$	$\phi (1,\phi (\omega ,0)+1)$	$\psi ({\mathrm{\Omega }}^{\omega }+1)$
$(0)(1,1)(2,1)(3,0)(1,1)(2,1)$	$\phi (2,\phi (\omega ,0)+1)$	$\psi ({\mathrm{\Omega }}^{\omega }+\mathrm{\Omega })$
$(0)(1,1)(2,1)(3,0)(1,1)(2,1)(2,1)$	$\phi (3,\phi (\omega ,0)+1)$	$\psi ({\mathrm{\Omega }}^{\omega }+{\mathrm{\Omega }}^2)$
$(0)(1,1)(2,1)(3,0)(1,1)(2,1)(3,0)$	$\phi (\omega ,1)$	$\psi ({\mathrm{\Omega }}^{\omega }\times 2)$
$(0)(1,1)(2,1)(3,0)(1,1)(2,1)(3,0)(1,1)(2,1)(3,0)$	$\phi (\omega ,2)$	$\psi ({\mathrm{\Omega }}^{\omega }\times 3)$
$(0)(1,1)(2,1)(3,0)(2,0)$	$\phi (\omega ,\omega )$	$\psi ({\mathrm{\Omega }}^{\omega }\times \omega )$
$(0)(1,1)(2,1)(3,0)(2,1)$	$\phi (\omega +1,0)$	$\psi ({\mathrm{\Omega }}^{\omega +1})$
$(0)(1,1)(2,1)(3,0)(2,1)(2,1)$	$\phi (\omega +2,0)$	$\psi ({\mathrm{\Omega }}^{\omega +2})$
$(0)(1,1)(2,1)(3,0)(2,1)(2,1)(2,1)$	$\phi (\omega +3,0)$	$\psi ({\mathrm{\Omega }}^{\omega +3})$
$(0)(1,1)(2,1)(3,0)(2,1)(3,0)$	$\phi (\omega \times 2,0)$	$\psi ({\mathrm{\Omega }}^{\omega \times 2})$
$(0)(1,1)(2,1)(3,0)(2,1)(3,0)(2,1)(3,0)$	$\phi (\omega \times 3,0)$	$\psi ({\mathrm{\Omega }}^{\omega \times 3})$
$(0)(1,1)(2,1)(3,0)(3,0)$	$\phi ({\omega }^2,0)$	$\psi ({\mathrm{\Omega }}^{{\omega }^2})$
$(0)(1,1)(2,1)(3,0)(4,1)$	$\phi (\phi (1,0),0)$	$\psi ({\mathrm{\Omega }}^{\psi (0)})$
$(0)(1,1)(2,1)(3,0)(4,1)(5,1)$	$\phi (\phi (2,0),0)$	$\psi ({\mathrm{\Omega }}^{\psi (\mathrm{\Omega })})$
$(0)(1,1)(2,1)(3,0)(4,1)(5,1)(6,0)$	$\phi (\phi (\omega ,0),0)$	$\psi ({\mathrm{\Omega }}^{\psi ({\mathrm{\Omega }}^{\omega })})$
$(0)(1,1)(2,1)(3,0)(4,1)(5,1)(6,0)(7,1)(8,1)(9,0)$	$\phi (\phi (\phi (\omega ,0),0),0)$	$\psi ({\mathrm{\Omega }}^{\psi ({\mathrm{\Omega }}^{\psi ({\mathrm{\Omega }}^{\omega })})})$
$(0)(1,1)(2,1)(3,1)$	$\phi (1,0,0)={\mathrm{\Gamma }}_0$	$\psi ({\mathrm{\Omega }}^{\mathrm{\Omega }})$
$(0)(1,1)(2,1)(3,1)(1,1)(2,1)(3,1)$	$\phi (1,0,1)={\mathrm{\Gamma }}_1$	$\psi ({\mathrm{\Omega }}^{\mathrm{\Omega }}\times 2)$
$(0)(1,1)(2,1)(3,1)(1,1)(2,1)(3,1)(1,1)(2,1)(3,1)$	$\phi (1,0,2)={\mathrm{\Gamma }}_2$	$\psi ({\mathrm{\Omega }}^{\mathrm{\Omega }}\times 3)$
$(0)(1,1)(2,1)(3,1)(2,0)$	$\phi (1,0,\omega )={\mathrm{\Gamma }}_{\omega }$	$\psi ({\mathrm{\Omega }}^{\mathrm{\Omega }}\times \omega )$
$(0)(1,1)(2,1)(3,1)(2,0)(3,1)(4,1)(5,1)$	$\phi (1,0,\phi (1,0,0))={\mathrm{\Gamma }}_{{\mathrm{\Gamma }}_0}$	$\psi ({\mathrm{\Omega }}^{\mathrm{\Omega }}\times \psi ({\mathrm{\Omega }}^{\mathrm{\Omega }}))$
$(0)(1,1)(2,1)(3,1)(2,0)(3,1)(4,1)(5,1)(4,0)(5,1)(6,1)(7,1)$	$\phi (1,0,\phi (1,0,\phi (1,0,0)))={\mathrm{\Gamma }}_{{\mathrm{\Gamma }}_{{\mathrm{\Gamma }}_0}}$	$\psi ({\mathrm{\Omega }}^{\mathrm{\Omega }}\times \psi ({\mathrm{\Omega }}^{\mathrm{\Omega }}\times \psi ({\mathrm{\Omega }}^{\mathrm{\Omega }})))$
$(0)(1,1)(2,1)(3,1)(2,1)$	$\phi (1,1,0)$	$\psi ({\mathrm{\Omega }}^{\mathrm{\Omega }+1})$
$(0)(1,1)(2,1)(3,1)(2,1)(2,1)$	$\phi (1,2,0)$	$\psi ({\mathrm{\Omega }}^{\mathrm{\Omega }+2})$
$(0)(1,1)(2,1)(3,1)(2,1)(3,0)$	$\phi (1,\omega ,0)$	$\psi ({\mathrm{\Omega }}^{\mathrm{\Omega }+\omega })$
$(0)(1,1)(2,1)(3,1)(2,1)(3,0)(4,1)(5,1)(6,1)(5,1)(6,0)$	$\phi (1,\phi (1,\omega ,0),0)$	$\psi ({\mathrm{\Omega }}^{\mathrm{\Omega }+\psi ({\mathrm{\Omega }}^{\mathrm{\Omega }+\omega })})$
$(0)(1,1)(2,1)(3,1)(2,1)(3,1)$	$\psi (2,0,0)$	$\psi ({\mathrm{\Omega }}^{\mathrm{\Omega }\times 2})$
$(0)(1,1)(2,1)(3,1)(2,1)(3,1)(2,1)(3,1)$	$\psi (3,0,0)$	$\psi ({\mathrm{\Omega }}^{\mathrm{\Omega }\times 3})$
$(0)(1,1)(2,1)(3,1)(3,0)$	$\phi (\omega ,0,0)$	$\psi ({\mathrm{\Omega }}^{\mathrm{\Omega }\times \omega })$
$(0)(1,1)(2,1)(3,1)(3,1)$	$\phi (1,0,0,0)$	$\psi ({\mathrm{\Omega }}^{{\mathrm{\Omega }}^2})$
$(0)(1,1)(2,1)(3,1)(3,1)(3,1)$	$\phi (1,0,0,0,0)$	$\psi ({\mathrm{\Omega }}^{{\mathrm{\Omega }}^3})$

BMS	MOCF
$(0)(1,1)(2,1)(3,1)(4,0)$	$\psi ({\mathrm{\Omega }}^{{\mathrm{\Omega }}^{\omega }})$
$(0)(1,1)(2,1)(3,1)(4,0)(5,1)$	$\psi ({\mathrm{\Omega }}^{{\mathrm{\Omega }}^{\psi (0)}})$
$(0)(1,1)(2,1)(3,1)(4,0)(5,1)(6,1)$	$\psi ({\mathrm{\Omega }}^{{\mathrm{\Omega }}^{\psi (\mathrm{\Omega })}})$
$(0)(1,1)(2,1)(3,1)(4,0)(5,1)(6,1)(7,1)$	$\psi ({\mathrm{\Omega }}^{{\mathrm{\Omega }}^{\psi ({\mathrm{\Omega }}^{\mathrm{\Omega }})}})$
$(0)(1,1)(2,1)(3,1)(4,1)$	$\psi ({\mathrm{\Omega }}^{{\mathrm{\Omega }}^{\mathrm{\Omega }}})$
$(0)(1,1)(2,1)(3,1)(4,1)(5,1)$	$\psi ({\mathrm{\Omega }}^{{\mathrm{\Omega }}^{{\mathrm{\Omega }}^{\mathrm{\Omega }}}})$
$(0)(1,1)(2,2)$	$\psi ({\psi }_1(0))$
$(0)(1,1)(2,2)(1,1)$	$\psi ({\psi }_1(0)+1)$
$(0)(1,1)(2,2)(1,1)(2,1)$	$\psi ({\psi }_1(0)+\mathrm{\Omega })$
$(0)(1,1)(2,2)(1,1)(2,1)(3,1)$	$\psi ({\psi }_1(0)+{\mathrm{\Omega }}^{\mathrm{\Omega }})$
$(0)(1,1)(2,2)(1,1)(2,2)$	$\psi ({\psi }_1(0)\times 2)$
$(0)(1,1)(2,2)(2,0)$	$\psi ({\psi }_1(0)\times \omega )$
$(0)(1,1)(2,2)(2,1)$	$\psi ({\psi }_1(0)\times \mathrm{\Omega })$
$(0)(1,1)(2,2)(2,1)(3,0)$	$\psi ({\psi }_1(0)\times {\mathrm{\Omega }}^{\omega })$
$(0)(1,1)(2,2)(2,1)(3,1)$	$\psi ({\psi }_1(0)\times {\mathrm{\Omega }}^{\mathrm{\Omega }})$
$(0)(1,1)(2,2)(2,1)(3,2)$	$\psi ({\psi }_1(0{)}^2)$
$(0)(1,1)(2,2)(2,1)(3,2)(3,0)$	$\psi ({\psi }_1(0{)}^{\omega })$
$(0)(1,1)(2,2)(2,1)(3,2)(3,1)(4,2)$	$\psi ({\psi }_1(0{)}^{{\psi }_1(0)})$
$(0)(1,1)(2,2)(2,2)$	$\psi ({\psi }_1(1))$
$(0)(1,1)(2,2)(3,0)$	$\psi ({\psi }_1(\omega ))$
$(0)(1,1)(2,2)(3,1)(4,2)$	$\psi ({\psi }_1({\psi }_1(0)))$
$(0)(1,1)(2,2)(3,2)$	$\psi ({\mathrm{\Omega }}_2)$
$(0)(1,1)(2,2)(3,2)(1,1)$	$\psi ({\mathrm{\Omega }}_2+\mathrm{\Omega })$
$(0)(1,1)(2,2)(3,2)(1,1)(2,2)$	$\psi ({\mathrm{\Omega }}_2+{\psi }_1(0))$
$(0)(1,1)(2,2)(3,2)(1,1)(2,2)(3,1)(4,2)$	$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\psi }_1(0)))$
$(0)(1,1)(2,2)(3,2)(1,1)(2,2)(3,2)$	$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2))$
$(0)(1,1)(2,2)(3,2)(2,0)$	$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2)\times \omega )$
$(0)(1,1)(2,2)(3,2)(2,1)(3,2)(4,2)$	$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2{)}^2)$
$(0)(1,1)(2,2)(3,2)(2,1)(3,2)(4,2)(3,0)$	$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2{)}^{\omega })$
$(0)(1,1)(2,2)(3,2)(2,1)(3,2)(4,2)(3,1)(4,2)(5,2)$	$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2{)}^{{\psi }_1({\mathrm{\Omega }}_2)})$
$(0)(1,1)(2,2)(3,2)(2,2)$	$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2+1))$
$(0)(1,1)(2,2)(3,2)(2,2)(3,0)$	$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2+\omega ))$
$(0)(1,1)(2,2)(3,2)(2,2)(3,1)(4,2)(5,2)$	$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2)))$
$(0)(1,1)(2,2)(3,2)(2,2)(3,1)(4,2)(5,2)(3,0)$	$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2)\times \omega ))$
$(0)(1,1)(2,2)(3,2)(2,2)(3,1)(4,2)(5,2)(4,0)$	$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2{)}^{\omega }))$
$(0)(1,1)(2,2)(3,2)(2,2)(3,1)(4,2)(5,2)(4,1)(5,2)(6,2)$	$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2{)}^{{\psi }_1({\mathrm{\Omega }}_2)}))$
$(0)(1,1)(2,2)(3,2)(2,2)(3,1)(4,2)(5,2)(4,2)$	$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2+1)))$
$(0)(1,1)(2,2)(3,2)(2,2)(3,1)(4,2)(5,2)(4,2)(5,0)$	$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2+\omega )))$
$(0)(1,1)(2,2)(3,2)(2,2)(3,1)(4,2)(5,2)(4,2)(5,0)(5,1)(6,2)(7,2)$	$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2))))$
$(0)(1,1)(2,2)(3,2)(2,2)(3,2)$	$\psi ({\mathrm{\Omega }}_2\times 2)$
$(0)(1,1)(2,2)(3,2)(3,0)$	$\psi ({\mathrm{\Omega }}_2\times \omega )$
$(0)(1,1)(2,2)(3,2)(3,1)(4,2)(5,2)$	$\psi ({\mathrm{\Omega }}_2\times {\psi }_1({\mathrm{\Omega }}_2))$
$(0)(1,1)(2,2)(3,2)(3,2)$	$\psi ({\mathrm{\Omega }}_2^2)$
$(0)(1,1)(2,2)(3,2)(4,0)$	$\psi ({\mathrm{\Omega }}_2^{\omega })$
$(0)(1,1)(2,2)(3,2)(4,2)$	$\psi ({\mathrm{\Omega }}_2^{{\mathrm{\Omega }}_2})$
$(0)(1,1)(2,2)(3,3)$	$\psi ({\psi }_2(0))$
$(0)(1,1)(2,2)(3,3)(4,3)$	$\psi ({\mathrm{\Omega }}_3)$
$(0)(1,1)(2,2)(3,3)(4,4)$	$\psi ({\psi }_3(0))$
$(0)(1,1,1)=(0)(1,1)(2,2)(3,3)\cdots$	$\psi ({\mathrm{\Omega }}_{\omega })$