Even and odd compositions with restricted parts

2024/05/06 by Jia Huang, Huang, Jia
Computer Science · #05A15 #05A19 #Advanced Algebra and Logic #Combinatorics (math.CO) #FOS: Mathematics #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2405.03477

openalex publication_date 2024/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A result of Legendre asserts that the difference between the numbers of (length) even and odd partitions of n into distinct parts is 0, 1, or -1; this also follows from Euler's pentagonal number theorem. We establish an analogous result for compositions and obtain some generalizations that are related to various entries in the On-Line Encyclopedia of Integer Sequences.

Related

• Compositions with restricted parts
• Combinatorial meaning of the number of the even parts in a partition of n into distinct parts
• On the partitions into distinct parts and odd parts
• Identities involving partitions with distinct odd parts and no parts congruent to 2 mod 4
• On Euler's Theorem