Choosing From A Negative Number Of Things?? #SoME2

Combinatorial Reciprocity Theorems by Mattias Beck and Raman Sanyal: An introductory look at negative binomial coefficients, and in general, combinatorial reciprocity. First, we explain how to formally justify binomial coefficients, then we explain what combinatorial reciprocity is, followed by an overview of some major examples and why it’s important. Covered topics include multisets, the generalized binomial theorem, proper n-colorings, orientations (acyclic and totally cyclic), compatibility of n-colorings and orientations, nowhere-zero flows, posets (partially ordered sets), mappings of posets preserving order, lattice points in polygons (and polytopes in general). In the pinned comment, I reference the negative binomial distribution. 00:00 Introduction 00:29 Chapter 1: Combinatorial Reciprocity 04:44 Chapter 2: Generating Functions 09:34 Chapter 3: More Examples of Combinatorial Reciprocity! 10:40 Chapter 3-1: Chromatic Polynomials 15:19 Chapter 3-2: Flow Polynomials 18:44 Chapter 3-3: Order Polynomials 21:48 Chapter 3-4: Ehrhart Polynomials 23:56 Conclusion Intro riff taken from: Nikolai Kapustin - 8 Concert Etudes, Op. 40: III. Toccatina Music Credit: Dusty Decks / Fall Call Timothy Infinite / Trumpet Man Sarah, the Illstrumentalist / Just Maintaining Gregory David / Corner Store Chill Cole / Amber Lights Guustavv / Coloration Luwaks / Reversed Beginning Giants’ Nest / Tiny Things Siine / Be Free With Me (instrumental) courtesy of