Integer partitions

Beyond Euler’s Partition Identity: The Algebraic Link Between Integer Partitions and Bell Polynomials via Infinite Products

Every math enthusiast has, at some point, been captivated by the sheer beauty of Euler's Partition Identity. This theore...

2026.05.20

数学

In this post, I will introduce the partition \(L\) function. DefinitionsLet \(n\) be a positive integer. Consider the sy...

2025.04.28

数学

In this post, I will introduce the partition zeta function. Definition【Definition】Let \(n\) be a positive integer and \(...

2025.04.28

数学

In this post, I will prove that\ where \(n\) is a positive integer. NotesIf \(\sigma \in S_n\) and \(\sigma' \in S_n\) a...

2024.07.01

数学