Counting SET-free sets

TL;DR

This paper investigates the enumeration of SET-free sets in an n-dimensional SET deck, revealing that the count satisfies specific polynomial conditions through algebraic reformulations.

Contribution

It introduces algebraic reformulations and reinterpretations to analyze the counting problem of SET-free sets, establishing polynomiality conditions.

Findings

Number of SET-free sets satisfies polynomiality conditions

Provides algebraic framework for counting SET-free sets

Advances understanding of combinatorial properties in SET decks

Abstract

We consider the following counting problem related to the card game SET: How many $k$-element SET-free sets are there in an $n$-dimensional SET deck? Through a series of algebraic reformulations and reinterpretations, we show the answer to this question satisfies two polynomiality conditions.