{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "a20af5f2-75ce-4e25-875f-f2e1e391806c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24-element Vector{Vector{Int64}}:\n",
       " [1, 2, 3, 4]\n",
       " [1, 2, 4, 3]\n",
       " [1, 3, 2, 4]\n",
       " [1, 3, 4, 2]\n",
       " [1, 4, 2, 3]\n",
       " [1, 4, 3, 2]\n",
       " [2, 1, 3, 4]\n",
       " [2, 1, 4, 3]\n",
       " [2, 3, 1, 4]\n",
       " [2, 3, 4, 1]\n",
       " [2, 4, 1, 3]\n",
       " [2, 4, 3, 1]\n",
       " [3, 1, 2, 4]\n",
       " [3, 1, 4, 2]\n",
       " [3, 2, 1, 4]\n",
       " [3, 2, 4, 1]\n",
       " [3, 4, 1, 2]\n",
       " [3, 4, 2, 1]\n",
       " [4, 1, 2, 3]\n",
       " [4, 1, 3, 2]\n",
       " [4, 2, 1, 3]\n",
       " [4, 2, 3, 1]\n",
       " [4, 3, 1, 2]\n",
       " [4, 3, 2, 1]"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Combinatorics\n",
    "permutations(1:4) |> collect"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "712fdd55-1122-4e2e-8651-e12109e2d149",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(σ, (σ(1), σ(2), σ(3), σ(4)), σ.([1, 2, 3, 4])) = ((1)(2)(3)(4), (1, 2, 3, 4), [1, 2, 3, 4])\n",
      "(σ, (σ(1), σ(2), σ(3), σ(4)), σ.([1, 2, 3, 4])) = ((1)(2)(3,4), (1, 2, 4, 3), [1, 2, 4, 3])\n",
      "(σ, (σ(1), σ(2), σ(3), σ(4)), σ.([1, 2, 3, 4])) = ((1)(2,3)(4), (1, 3, 2, 4), [1, 3, 2, 4])\n",
      "(σ, (σ(1), σ(2), σ(3), σ(4)), σ.([1, 2, 3, 4])) = ((1)(2,3,4), (1, 3, 4, 2), [1, 3, 4, 2])\n",
      "(σ, (σ(1), σ(2), σ(3), σ(4)), σ.([1, 2, 3, 4])) = ((1)(2,4,3), (1, 4, 2, 3), [1, 4, 2, 3])\n",
      "(σ, (σ(1), σ(2), σ(3), σ(4)), σ.([1, 2, 3, 4])) = ((1)(2,4)(3), (1, 4, 3, 2), [1, 4, 3, 2])\n",
      "(σ, (σ(1), σ(2), σ(3), σ(4)), σ.([1, 2, 3, 4])) = ((1,2)(3)(4), (2, 1, 3, 4), [2, 1, 3, 4])\n",
      "(σ, (σ(1), σ(2), σ(3), σ(4)), σ.([1, 2, 3, 4])) = ((1,2)(3,4), (2, 1, 4, 3), [2, 1, 4, 3])\n",
      "(σ, (σ(1), σ(2), σ(3), σ(4)), σ.([1, 2, 3, 4])) = ((1,2,3)(4), (2, 3, 1, 4), [2, 3, 1, 4])\n",
      "(σ, (σ(1), σ(2), σ(3), σ(4)), σ.([1, 2, 3, 4])) = ((1,2,3,4), (2, 3, 4, 1), [2, 3, 4, 1])\n",
      "(σ, (σ(1), σ(2), σ(3), σ(4)), σ.([1, 2, 3, 4])) = ((1,2,4,3), (2, 4, 1, 3), [2, 4, 1, 3])\n",
      "(σ, (σ(1), σ(2), σ(3), σ(4)), σ.([1, 2, 3, 4])) = ((1,2,4)(3), (2, 4, 3, 1), [2, 4, 3, 1])\n",
      "(σ, (σ(1), σ(2), σ(3), σ(4)), σ.([1, 2, 3, 4])) = ((1,3,2)(4), (3, 1, 2, 4), [3, 1, 2, 4])\n",
      "(σ, (σ(1), σ(2), σ(3), σ(4)), σ.([1, 2, 3, 4])) = ((1,3,4,2), (3, 1, 4, 2), [3, 1, 4, 2])\n",
      "(σ, (σ(1), σ(2), σ(3), σ(4)), σ.([1, 2, 3, 4])) = ((1,3)(2)(4), (3, 2, 1, 4), [3, 2, 1, 4])\n",
      "(σ, (σ(1), σ(2), σ(3), σ(4)), σ.([1, 2, 3, 4])) = ((1,3,4)(2), (3, 2, 4, 1), [3, 2, 4, 1])\n",
      "(σ, (σ(1), σ(2), σ(3), σ(4)), σ.([1, 2, 3, 4])) = ((1,3)(2,4), (3, 4, 1, 2), [3, 4, 1, 2])\n",
      "(σ, (σ(1), σ(2), σ(3), σ(4)), σ.([1, 2, 3, 4])) = ((1,3,2,4), (3, 4, 2, 1), [3, 4, 2, 1])\n",
      "(σ, (σ(1), σ(2), σ(3), σ(4)), σ.([1, 2, 3, 4])) = ((1,4,3,2), (4, 1, 2, 3), [4, 1, 2, 3])\n",
      "(σ, (σ(1), σ(2), σ(3), σ(4)), σ.([1, 2, 3, 4])) = ((1,4,2)(3), (4, 1, 3, 2), [4, 1, 3, 2])\n",
      "(σ, (σ(1), σ(2), σ(3), σ(4)), σ.([1, 2, 3, 4])) = ((1,4,3)(2), (4, 2, 1, 3), [4, 2, 1, 3])\n",
      "(σ, (σ(1), σ(2), σ(3), σ(4)), σ.([1, 2, 3, 4])) = ((1,4)(2)(3), (4, 2, 3, 1), [4, 2, 3, 1])\n",
      "(σ, (σ(1), σ(2), σ(3), σ(4)), σ.([1, 2, 3, 4])) = ((1,4,2,3), (4, 3, 1, 2), [4, 3, 1, 2])\n",
      "(σ, (σ(1), σ(2), σ(3), σ(4)), σ.([1, 2, 3, 4])) = ((1,4)(2,3), (4, 3, 2, 1), [4, 3, 2, 1])\n"
     ]
    }
   ],
   "source": [
    "using Permutations\n",
    "\n",
    "for σ in PermGen(4)\n",
    "    @show σ, (σ(1), σ(2), σ(3), σ(4)), σ.([1,2,3,4])\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "de353afa-cc96-4e26-a6d2-4e48650e058d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24-element Vector{Permutation}:\n",
       " (1)(2)(3)(4)\n",
       " (1)(2)(3,4)\n",
       " (1)(2,3)(4)\n",
       " (1)(2,3,4)\n",
       " (1)(2,4,3)\n",
       " (1)(2,4)(3)\n",
       " (1,2)(3)(4)\n",
       " (1,2)(3,4)\n",
       " (1,2,3)(4)\n",
       " (1,2,3,4)\n",
       " (1,2,4,3)\n",
       " (1,2,4)(3)\n",
       " (1,3,2)(4)\n",
       " (1,3,4,2)\n",
       " (1,3)(2)(4)\n",
       " (1,3,4)(2)\n",
       " (1,3)(2,4)\n",
       " (1,3,2,4)\n",
       " (1,4,3,2)\n",
       " (1,4,2)(3)\n",
       " (1,4,3)(2)\n",
       " (1,4)(2)(3)\n",
       " (1,4,2,3)\n",
       " (1,4)(2,3)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S4 = collect(PermGen(4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "68765bab-40b6-4140-a5e9-c41baa1e721b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1)(2,3)(4)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "σ = S4[3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "9575364c-1fc7-4855-8c4d-e85f265cf83a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1,4,2)(3)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "τ = S4[20]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "f75e86cd-6bf0-4160-8fe7-85749161e98b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1,4,3,2)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "σ*τ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "667a2b82-9353-4d0f-9725-1f006f65a787",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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