{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Combinatorics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "num_diagrams_small_form (generic function with 3 methods)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "function num_diagrams(m::Int, e::Int, u::Int = 0, t::Int = 0)\n",
    "    n = e + u + t\n",
    "    return Int(factorial(3n-3) / factorial(2n-1)) * binomial(m+3n-3, 3n-3) * factorial(m) * factorial(e) * factorial(u) * factorial(t)\n",
    "end\n",
    "\n",
    "function num_diagrams_small_form(m::Int, e::Int, u::Int = 0, t::Int = 0)\n",
    "    n = e + u + t\n",
    "    return Int(factorial(m+3n-3) / factorial(2n-1)) * factorial(e) * factorial(u) * factorial(t)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8\n",
      "8\n"
     ]
    }
   ],
   "source": [
    "# Trident:\n",
    "println(num_diagrams(1, 2))\n",
    "println(num_diagrams_small_form(1, 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2, 6, 24, 120, 720, 5040, 40320]\n",
      "[2, 6, 24, 120, 720, 5040, 40320]\n"
     ]
    }
   ],
   "source": [
    "# n-Photon Compton:\n",
    "println([num_diagrams(n, 1) for n in 2:8])\n",
    "println([num_diagrams_small_form(n, 1) for n in 2:8])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2, 36, 1728, 158400, 23587200, 5181926400]\n",
      "[2, 36, 1728, 158400, 23587200, 5181926400]\n"
     ]
    }
   ],
   "source": [
    "# fermion scattering\n",
    "println([num_diagrams(0, n) for n in 2:7])\n",
    "println([num_diagrams_small_form(0, n) for n in 2:7])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\\rowcolor[HTML]{9B9B9B}1 && 1 & 0 & 0 & 1 & 1 & 2 & 6 & 24 & 120 \\\\ \\hline\n",
      "\\rowcolor[HTML]{C0C0C0}2 && 1 & 1 & 0 & 1 & 4 & 20 & 120 & 840 & 6720 \\\\ \\hline\n",
      "\\rowcolor[HTML]{9B9B9B}2 && 2 & 0 & 0 & 2 & 8 & 40 & 240 & 1680 & 13440 \\\\ \\hline\n",
      "\\rowcolor[HTML]{C0C0C0}3 && 1 & 1 & 1 & 6 & 42 & 336 & 3024 & 30240 & 332640 \\\\ \\hline\n",
      "\\rowcolor[HTML]{9B9B9B}3 && 2 & 1 & 0 & 12 & 84 & 672 & 6048 & 60480 & 665280 \\\\ \\hline\n",
      "\\rowcolor[HTML]{C0C0C0}3 && 3 & 0 & 0 & 36 & 252 & 2016 & 18144 & 181440 & 1995840 \\\\ \\hline\n",
      "\\rowcolor[HTML]{9B9B9B}4 && 2 & 1 & 1 & 144 & 1440 & 15840 & 190080 & 2471040 & 34594560 \\\\ \\hline\n",
      "\\rowcolor[HTML]{C0C0C0}4 && 2 & 2 & 0 & 288 & 2880 & 31680 & 380160 & 4942080 & 69189120 \\\\ \\hline\n",
      "\\rowcolor[HTML]{9B9B9B}4 && 3 & 1 & 0 & 432 & 4320 & 47520 & 570240 & 7413120 & 103783680 \\\\ \\hline\n",
      "\\rowcolor[HTML]{C0C0C0}4 && 4 & 0 & 0 & 1728 & 17280 & 190080 & 2280960 & 29652480 & 415134720 \\\\ \\hline\n"
     ]
    }
   ],
   "source": [
    "# tables\n",
    "i = 0\n",
    "nums = [[1, 0, 0], [1, 1, 0], [2, 0, 0], [1, 1, 1], [2, 1, 0], [3, 0, 0], [2, 1, 1], [2, 2, 0], [3, 1, 0], [4, 0, 0]]\n",
    "for (e, u, t) in nums\n",
    "    i += 1\n",
    "    if (u + t + e == 0) continue end\n",
    "    if (i % 2 == 0) \n",
    "        print(\"\\\\rowcolor[HTML]{C0C0C0}\")\n",
    "    else\n",
    "        print(\"\\\\rowcolor[HTML]{9B9B9B}\")\n",
    "    end\n",
    "    println(\"$(e + u + t) && $e & $u & $t & $(num_diagrams(0, e, u, t)) & $(num_diagrams(1, e, u, t)) & $(num_diagrams(2, e, u, t)) & $(num_diagrams(3, e, u, t)) & $(num_diagrams(4, e, u, t)) & $(num_diagrams(5, e, u, t)) \\\\\\\\ \\\\hline\")\n",
    "end"
   ]
  }
 ],
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