two-row BMS, PSS (\(\varepsilon_0\) ~ \(\mathrm{BO} = \psi(\Omega_\omega)\))
\(\varepsilon_0\) ~ \(\mathrm{CO} = \zeta_0\)
\(\varepsilon_0\) ~ \(\varepsilon_1\)
Using \(\forall \alpha< \varepsilon_0, \omega^\alpha= \psi(\alpha)\) in BOCF.
| BMS | BOCF | NN |
|---|---|---|
| \(()(1,1)\) | \(\psi(\psi_1(0))\) | \(\varepsilon_0\) |
| \(()(1,1)()(1,1)\) | \(\psi(\psi_1(0))2\) | \(\varepsilon_0 2\) |
| \(()(1,1)(1)\) | \(\psi(\psi_1(0)+1)\) | \(\omega^{\varepsilon_0+1}\) |
| \(()(1,1)(1)(1)\) | \(\psi(\psi_1(0)+2)\) | \(\omega^{\varepsilon_0+2}\) |
| \(()(1,1)(1)(2)\) | \(\psi(\psi_1(0)+\omega)\) | \(\omega^{\varepsilon_0+\omega}\) |
| \(()(1,1)(1)(2)(2)\) | \(\psi(\psi_1(0)+\omega^2)\) | \(\omega^{\varepsilon_0+\omega^2}\) |
| \(()(1,1)(1)(2)(3)\) | \(\psi(\psi_1(0)+\omega^3)\) | \(\omega^{\varepsilon_0+\omega^3}\) |
| \(()(1,1)(1)(2,1)\) | \(\psi(\psi_1(0)+\psi(\psi_1(0)))\) | \(\omega^{\varepsilon_0 2}\) |
| \(()(1,1)(1)(2,1)(1)(2,1)\) | \(\psi(\psi_1(0)+\psi(\psi_1(0))2)\) | \(\omega^{\varepsilon_0 3}\) |
| \(()(1,1)(1)(2,1)(2)\) | \(\psi(\psi_1(0)+\psi(\psi_1(0)+1))\) | \(\omega^{\omega^{\varepsilon_0+1}}\) |
| \(()(1,1)(1)(2,1)(2)(1)(2,1)\) | \(\psi(\psi_1(0)+\psi(\psi_1(0)+1)+\psi(\psi_1(0)))\) | \(\omega^{\omega^{\varepsilon_0+1}+\varepsilon_0}\) |
| \(()(1,1)(1)(2,1)(2)(1)(2,1)(1)(2,1)\) | \(\psi(\psi_1(0)+\psi(\psi_1(0)+1)+\psi(\psi_1(0))2)\) | \(\omega^{\omega^{\varepsilon_0+1}+\varepsilon_0 2}\) |
| \(()(1,1)(1)(2,1)(2)(1)(2,1)(2)\) | \(\psi(\psi_1(0)+\psi(\psi_1(0)+1)2)\) | \(\omega^{\omega^{\varepsilon_0+1} 2}\) |
| \(()(1,1)(1)(2,1)(2)(2)\) | \(\psi(\psi_1(0)+\psi(\psi_1(0)+2))\) | \(\omega^{\omega^{\varepsilon_0+2}}\) |
| \(()(1,1)(1)(2,1)(2)(3)\) | \(\psi(\psi_1(0)+\psi(\psi_1(0)+\omega))\) | \(\omega^{\omega^{\varepsilon_0+\omega}}\) |
| \(()(1,1)(1)(2,1)(2)(3,1)\) | \(\psi(\psi_1(0)+\psi(\psi_1(0)+\psi(\psi_1(0))))\) | \(\omega^{\omega^{\varepsilon_0 2}}\) |
| \(()(1,1)(1,1)\) | \(\psi(\psi_1(0)2)\) | \(\varepsilon_1\) |
\(\varepsilon_1\) ~ \(\varepsilon_{\varepsilon_0}\)
| BMS | BOCF | NN |
|---|---|---|
| \(()(1,1)(1,1)\) | \(\psi(\psi_1(0)2)\) | \(\varepsilon_1\) |
| \(()(1,1)(1,1)(1)\) | \(\psi(\psi_1(0)2+1)\) | \(\omega^{\varepsilon_1+1}\) |
| \(()(1,1)(1,1)(1)(2,1)\) | \(\psi(\psi_1(0)2+\psi(\psi_1(0)))\) | \(\omega^{\varepsilon_1+\varepsilon_0}\) |
| \(()(1,1)(1,1)(1)(2,1)(2,1)\) | \(\psi(\psi_1(0)2+\psi(\psi_1(0)2))\) | \(\omega^{\varepsilon_1 2}\) |
| \(()(1,1)(1,1)(1)(2,1)(2,1)(2)(3,1)(3,1)\) | \(\psi(\psi_1(0)2+\psi(\psi_1(0)2+\psi(\psi_1(0)2)))\) | \(\omega^{\omega^{\varepsilon_1 2}}\) |
| \(()(1,1)(1,1)(1,1)\) | \(\psi(\psi_1(0)3)\) | \(\varepsilon_2\) |
| \(()(1,1)(2)\) | \(\psi(\psi_1(1))\) | \(\varepsilon_\omega\) |
| \(()(1,1)(2)(1)(2,1)(3)\) | \(\psi(\psi_1(1)+\psi(\psi_1(1)))\) | \(\omega^{\varepsilon_\omega 2}\) |
| \(()(1,1)(2)(1,1)\) | \(\psi(\psi_1(1)+\psi_1(0))\) | \(\varepsilon_{\omega+1}\) |
| \(()(1,1)(2)(1,1)(1,1)\) | \(\psi(\psi_1(1)+\psi_1(0)2)\) | \(\varepsilon_{\omega+2}\) |
| \(()(1,1)(2)(1,1)(2)\) | \(\psi(\psi_1(1)2)\) | \(\varepsilon_{\omega 2}\) |
| \(()(1,1)(2)(2)\) | \(\psi(\psi_1(2))\) | \(\varepsilon_{\omega^2}\) |
| \(()(1,1)(2)(3)\) | \(\psi(\psi_1(\omega))\) | \(\varepsilon_{\omega^\omega}\) |
| \(()(1,1)(2)(3)(4)\) | \(\psi(\psi_1(\omega^\omega))\) | \(\varepsilon_{\omega^{\omega^\omega}}\) |
| \(()(1,1)(2)(3,1)\) | \(\psi(\psi_1(\psi(\psi_1(0))))\) | \(\varepsilon_{\varepsilon_0}\) |
\(\varepsilon_{\varepsilon_0}\) ~ \(\mathrm{CO} = \zeta_0\)
| BMS | BOCF | NN |
|---|---|---|
| \(()(1,1)(2)(3,1)\) | \(\psi(\psi_1(\psi(\psi_1(0))))\) | \(\varepsilon_{\varepsilon_0}\) |
| \(()(1,1)(2)(1)(2,1)(3)\) | \(\psi(\psi_1(1)+\psi(\psi_1(1)))\) | \(\omega^{\varepsilon_\omega 2}\) |
| \(()(1,1)(2)(1,1)\) | \(\psi(\psi_1(1)+\psi_1(0))\) | \(\varepsilon_{\omega+1}\) |
| \(()(1,1)(2)(1,1)(1,1)\) | \(\psi(\psi_1(1)+\psi_1(0)2)\) | \(\varepsilon_{\omega+2}\) |
| \(()(1,1)(2)(1,1)(2)\) | \(\psi(\psi_1(1)2)\) | \(\varepsilon_{\omega 2}\) |
| \(()(1,1)(2)(2)\) | \(\psi(\psi_1(2))\) | \(\varepsilon_{\omega^2}\) |
| \(()(1,1)(2)(3)\) | \(\psi(\psi_1(\omega))\) | \(\varepsilon_{\omega^\omega}\) |
| \(()(1,1)(2)(3)(4)\) | \(\psi(\psi_1(\omega^\omega))\) | \(\varepsilon_{\omega^{\omega^\omega}}\) |
| \(()(1,1)(2)(3,1)\) | \(\psi(\psi_1(\psi(\psi_1(0))))\) | \(\varepsilon_{\varepsilon_0}\) |
| \(()(1,1)(2)(3,1)(1,1)\) | \(\psi(\psi_1(\psi(\psi_1(0)))+\psi_1(0))\) | \(\varepsilon_{\varepsilon_0+1}\) |
| \(()(1,1)(2)(3,1)(1,1)(2)(3,1)\) | \(\psi(\psi_1(\psi(\psi_1(0)))2)\) | \(\varepsilon_{\varepsilon_0 2}\) |
| \(()(1,1)(2)(3,1)(2)\) | \(\psi(\psi_1(\psi(\psi_1(0))+1))\) | \(\varepsilon_{\omega^{\varepsilon_0+1}}\) |
| \(()(1,1)(2)(3,1)(2)(1,1)(2)(3,1)(2)\) | \(\psi(\psi_1(\psi(\psi_1(0))+1)2)\) | \(\varepsilon_{\omega^{\varepsilon_0+1}2}\) |
| \(()(1,1)(2)(3,1)(2)(2)\) | \(\psi(\psi_1(\psi(\psi_1(0))+2))\) | \(\varepsilon_{\omega^{\varepsilon_0+2}}\) |
| \(()(1,1)(2)(3,1)(2)(3)\) | \(\psi(\psi_1(\psi(\psi_1(0))+\omega))\) | \(\varepsilon_{\omega^{\varepsilon_0+\omega}}\) |
| \(()(1,1)(2)(3,1)(2)(3,1)\) | \(\psi(\psi_1(\psi(\psi_1(0))2)\) | \(\varepsilon_{\omega^{\varepsilon_0 2}}\) |
| \(()(1,1)(2)(3,1)(3)\) | \(\psi(\psi_1(\psi(\psi_1(0)+1))\) | \(\varepsilon_{\omega^{\omega^{\varepsilon_0+1}}}\) |
| \(()(1,1)(2)(3,1)(3)(4)\) | \(\psi(\psi_1(\psi(\psi_1(0)+\omega))\) | \(\varepsilon_{\omega^{\omega^{\varepsilon_0+\omega}}}\) |
| \(()(1,1)(2)(3,1)(3)(4,1)\) | \(\psi(\psi_1(\psi(\psi_1(0)+\psi(\psi_1(0))))\) | \(\varepsilon_{\omega^{\omega^{\varepsilon_0 2}}}\) |
| \(()(1,1)(2)(3,1)(3,1)\) | \(\psi(\psi_1(\psi(\psi_1(0)2))\) | \(\varepsilon_{\varepsilon_1}\) |
| \(()(1,1)(2)(3,1)(4)\) | \(\psi(\psi_1(\psi(\psi_1(1)))\) | \(\varepsilon_{\varepsilon_\omega}\) |
| \(()(1,1)(2)(3,1)(4)(5,1)\) | \(\psi(\psi_1(\psi(\psi_1(\psi(\psi_1(0)))))\) | \(\varepsilon_{\varepsilon_{\varepsilon_0}}\) |
| \(()(1,1)(2,1)\) | \(\psi(\psi_1(\psi_1(0)))\) | \(\mathrm{CO} = \zeta_0\) |
\(\zeta_0\) ~ \(\mathrm{FSO} = \Gamma_0 = \varphi(1,0,0)\)
\(\zeta_0\) ~ \(\mathrm{HCO} = \varphi(\omega,0)\)
Using \(\forall \alpha< \psi_1(\psi_2(0)) = \varepsilon_{\Omega+1}, \omega^{\Omega+\alpha} = \psi_1(\alpha)\) in BOCF.
| BMS | BOCF | NN |
|---|---|---|
| \(()(1,1)(2,1)\) | \(\psi(\Omega^2)\) | \(\zeta_0\) |
| \(()(1,1)(2,1)(1)\) | \(\psi(\Omega^2+1)\) | \(\omega^{\zeta_0+1}\) |
| \(()(1,1)(2,1)(1)(2,1)\) | \(\psi(\Omega^2+\psi(\Omega))\) | \(\omega^{\zeta_0+\varepsilon_0}\) |
| \(()(1,1)(2,1)(1)(2,1)(3,1)\) | \(\psi(\Omega^2+\psi(\Omega^2))\) | \(\omega^{\zeta_0 2}\) |
| \(()(1,1)(2,1)(1,1)\) | \(\psi(\Omega^2+\Omega)\) | \(\varepsilon_{\zeta_0+1}\) |
| \(()(1,1)(2,1)(1,1)(2)\) | \(\psi(\Omega^2+\Omega\omega))\) | \(\varepsilon_{\zeta_0+\omega}\) |
| \(()(1,1)(2,1)(1,1)(2)(3,1)(4,1)\) | \(\psi(\Omega^2+\Omega\psi(\Omega^2))\) | \(\varepsilon_{\zeta_0 2}\) |
| \(()(1,1)(2,1)(1,1)(2)(3,1)(4,1)(3,1)\) | \(\psi(\Omega^2+\Omega\psi(\Omega^2+\Omega))\) | \(\varepsilon_{\varepsilon_{\zeta_0+1}}\) |
| \(()(1,1)(2,1)(1,1)(2,1)\) | \(\psi(\Omega^22)\) | \(\zeta_1\) |
| \(()(1,1)(2,1)(1,1)(2,1)(1,1)\\(2)(3,1)(4,1)(3,1)(4,1)\) | \(\psi(\Omega^2 2+\Omega\psi(\Omega^2 2))\) | \(\varepsilon_{\zeta_1 2}\) |
| \(()(1,1)(2,1)(1,1)(2,1)(1,1)(2,1)\) | \(\psi(\Omega^23)\) | \(\zeta_2\) |
| \(()(1,1)(2,1)(2)\) | \(\psi(\Omega^2\omega)\) | \(\zeta_\omega\) |
| \(()(1,1)(2,1)(2)(1,1)(2,1)\) | \(\psi(\Omega^2\omega+\Omega^2)\) | \(\zeta_{\omega+1}\) |
| \(()(1,1)(2,1)(2)(1,1)(2,1)(2)\) | \(\psi(\Omega^2\omega 2)\) | \(\zeta_{\omega 2}\) |
| \(()(1,1)(2,1)(2)(2)\) | \(\psi(\Omega^2\omega^2)\) | \(\zeta_{\omega^2}\) |
| \(()(1,1)(2,1)(2)(3)\) | \(\psi(\Omega^2\omega^\omega)\) | \(\zeta_{\omega^\omega}\) |
| \(()(1,1)(2,1)(2)(3,1)\) | \(\psi(\Omega^2\psi(\Omega))\) | \(\zeta_{\varepsilon_0}\) |
| \(()(1,1)(2,1)(2)(3,1)(4,1)\) | \(\psi(\Omega^2\psi(\Omega^2))\) | \(\zeta_{\zeta_0}\) |
| \(()(1,1)(2,1)(2,1)\) | \(\psi(\Omega^3)\) | \(\eta_0\) |
| \(()(1,1)(2,1)(2,1)(1,1)\) | \(\psi(\Omega^3+\Omega)\) | \(\varepsilon_{\eta_0+1}\) |
| \(()(1,1)(2,1)(2,1)(1,1)(2,1)\) | \(\psi(\Omega^3+\Omega^2)\) | \(\zeta_{\eta_0+1}\) |
| \(()(1,1)(2,1)(2,1)(1,1)(2,1)(2,1)\) | \(\psi(\Omega^32)\) | \(\eta_1\) |
| \(()(1,1)(2,1)(2,1)(2)\) | \(\psi(\Omega^3\omega)\) | \(\eta_\omega\) |
| \(()(1,1)(2,1)(2,1)(2)(3,1)(4,1)(4,1)\) | \(\psi(\Omega^3\psi(\Omega^3))\) | \(\eta_{\eta_0}\) |
| \(()(1,1)(2,1)(2,1)(2,1)\) | \(\psi(\Omega^4)\) | \(\varphi(4,0)\) |
| \(()(1,1)(2,1)(3)\) | \(\psi(\Omega^\omega)\) | \(\mathrm{HCO} = \varphi(\omega,0)\) |
\(\varphi(\omega,0)\) ~ \(\mathrm{FSO} = \Gamma_0 = \varphi(1,0,0)\)
| BMS | BOCF | NN |
|---|---|---|
| \(()(1,1)(2,1)(3)\) | \(\psi(\Omega^\omega)\) | \(\varphi(\omega,0)\) |
| \(()(1,1)(2,1)(3)(1,1)\) | \(\psi(\Omega^\omega+\Omega)\) | \(\varepsilon_{\varphi(\omega,0)+1}\) |
| \(()(1,1)(2,1)(3)(1,1)(2,1)\) | \(\psi(\Omega^\omega+\Omega^2)\) | \(\zeta_{\varphi(\omega,0)+1}\) |
| \(()(1,1)(2,1)(3)(1,1)(2,1)(2,1)\) | \(\psi(\Omega^\omega+\Omega^3)\) | \(\eta_{\varphi(\omega,0)+1}\) |
| \(()(1,1)(2,1)(3)(1,1)(2,1)(3)\) | \(\psi(\Omega^\omega 2)\) | \(\varphi(\omega,1)\) |
| \(()(1,1)(2,1)(3)(2)\) | \(\psi(\Omega^\omega\omega)\) | \(\varphi(\omega,\omega)\) |
| \(()(1,1)(2,1)(3)(2)(3,1)\) | \(\psi(\Omega^\omega\psi(\Omega))\) | \(\varphi(\omega,\varepsilon_0)\) |
| \(()(1,1)(2,1)(3)(2)(3,1)(4,1)\) | \(\psi(\Omega^\omega\psi(\Omega^2))\) | \(\varphi(\omega,\zeta_0)\) |
| \(()(1,1)(2,1)(3)(2)(3,1)(4,1)(5)\) | \(\psi(\Omega^\omega\psi(\Omega^\omega))\) | \(\varphi(\omega,\varphi(\omega,0))\) |
| \(()(1,1)(2,1)(3)(2,1)\) | \(\psi(\Omega^{\omega+1})\) | \(\varphi(\omega+1,0)\) |
| \(()(1,1)(2,1)(3)(2,1)(1,1)(2,1)(3)(2,1)\) | \(\psi(\Omega^{\omega+1}2)\) | \(\varphi(\omega+1,1)\) |
| \(()(1,1)(2,1)(3)(2,1)(2)\) | \(\psi(\Omega^{\omega+1}\omega)\) | \(\varphi(\omega+1,\omega)\) |
| \(()(1,1)(2,1)(3)(2,1)(2)(3,1)(4,1)(5)(4,1)\) | \(\psi(\Omega^{\omega+1}\psi(\Omega^{\omega+1}))\) | \(\varphi(\omega+1,\varphi(\omega+1,0))\) |
| \(()(1,1)(2,1)(3)(2,1)(2,1)\) | \(\psi(\Omega^{\omega+2})\) | \(\varphi(\omega+2,0)\) |
| \(()(1,1)(2,1)(3)(2,1)(3)\) | \(\psi(\Omega^{\omega 2})\) | \(\varphi(\omega 2,0)\) |
| \(()(1,1)(2,1)(3)(3)\) | \(\psi\left(\Omega^{\omega^2}\right)\) | \(\varphi(\omega^2,0)\) |
| \(()(1,1)(2,1)(3)(4)\) | \(\psi\left(\Omega^{\omega^\omega}\right)\) | \(\varphi(\omega^\omega,0)\) |
| \(()(1,1)(2,1)(3)(4,1)\) | \(\psi\left(\Omega^{\psi(\Omega)}\right)\) | \(\varphi(\varepsilon_0,0)\) |
| \(()(1,1)(2,1)(3)(4,1)(5,1)\) | \(\psi\left(\Omega^{\psi(\Omega^2)}\right)\) | \(\varphi(\zeta_0,0)\) |
| \(()(1,1)(2,1)(3)(4,1)(5,1)(6)\) | \(\psi\left(\Omega^{\psi(\Omega^\omega)}\right)\) | \(\varphi(\varphi(\omega,0),0)\) |
| \(()(1,1)(2,1)(3)(4,1)(5,1)(6)(7,1)(8,1)\) | \(\psi\left(\Omega^{\psi\left(\Omega^{\psi(\Omega^2)}\right)}\right)\) | \(\varphi(\varphi(\zeta_0,0),0)\) |
| \(()(1,1)(2,1)(3,1)\) | \(\psi(\Omega^\Omega)\) | \(\mathrm{FSO} = \Gamma_0\) |