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Finite Cardinalities of Misère Quotients

Simon Rubinstein-Salzedo, Stephen Zhou

Abstract

We find that partisan misère quotients can have any finite cardinality other than 3, answering a question of Allen. This contrasts with impartial misère quotients, which must have even cardinality.

Finite Cardinalities of Misère Quotients

Abstract

We find that partisan misère quotients can have any finite cardinality other than 3, answering a question of Allen. This contrasts with impartial misère quotients, which must have even cardinality.
Paper Structure (4 sections, 21 theorems, 8 equations, 1 table)

This paper contains 4 sections, 21 theorems, 8 equations, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Quotients of Sums of Blue Mutant Flowers
  4. There is No Misère Quotient of Order 3

Key Result

Theorem 1.1

Let $n \in \mathbb{N}$, with $n \neq 3$. Then there exists a closed set $\mathscr{A}$ such that $|\mathcal{Q}(\mathscr{A})| = n$.

Theorems & Definitions (41)

  • Theorem 1.1
  • Theorem 1.2
  • Definition 2.1
  • Definition 2.2
  • Theorem 2.3
  • Theorem 2.4
  • proof
  • Theorem 2.5
  • Lemma 2.6
  • proof
  • ...and 31 more