notebooks/num_diagrams.ipynb

@@ -0,0 +1,123 @@
+{
+ "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
+}