Permutations avoiding 4321 and 3241 have an algebraic generating function

TL;DR

This paper proves that permutations avoiding the patterns 4321 and 3241 have an algebraic generating function, confirming a conjecture by Vladimir Kruchinin.

Contribution

It establishes the algebraicity of the generating function for permutations avoiding two specific patterns, advancing understanding in permutation pattern enumeration.

Findings

Generated algebraic functions for these pattern-avoiding permutations

Confirmed Kruchinin's conjecture on the algebraic nature of the generating function

Provides new insights into permutation pattern avoidance enumeration

Abstract

We show that permutations avoiding both of the (classical) patterns 4321 and 3241 have the algebraic generating function conjectured by Vladimir Kruchinin.