{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Combinatorics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "num_diagrams (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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trident:\n",
    "num_diagrams(1, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7-element Vector{Int64}:\n",
       "     2\n",
       "     6\n",
       "    24\n",
       "   120\n",
       "   720\n",
       "  5040\n",
       " 40320"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# n-Photon Compton:\n",
    "[num_diagrams(n, 1) for n in 2:8]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6-element Vector{Int64}:\n",
       "          2\n",
       "         36\n",
       "       1728\n",
       "     158400\n",
       "   23587200\n",
       " 5181926400"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# fermion scattering\n",
    "[num_diagrams(0, n) for n in 2:7]"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 1.9.4",
   "language": "julia",
   "name": "julia-1.9"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.9.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}