The Interrobang Operator: a Notation for Partial Permutations

2026/07/29 by Jon Carroll, Nic Carroll · 1 voice
Mathematics · Computer Science · #Advanced Combinatorial Mathematics #semigroups and automata theory #Advanced Mathematical Identities #Unary operation #Notation #Sequence (biology) #Natural number #Operator (biology) #Permutation (music) #Class (philosophy)

paper · doi:10.5281/zenodo.21675660

openalex publication_date 2026/07/29 · openalex created_date 2026/07/30 · openalex updated_date 2026/07/30

Abstract

We propose the interrobang ‽ (U+203D) as a unary postfix operator n‽, defined as the sum from k=0 to n of n!/k!: the number of ways to arrange any number, from zero up to all, of n distinct objects in a row. This is OEIS sequence A000522, a sequence with real recurring uses in combinatorics but no dedicated symbol. We give the definition, seven elementary properties with proofs, and an honest account of why the natural alternative notation is unavailable.

Discussions

• The sequence A000522 (1, 2, 5, 16, 65, 326, 1957, ...), defined by $$a(n) = \sum_{k=0}^n \frac{n!}{k!}$$ counts the number of ways to arrange any number (from 0 up to all) of n distinct objects in a r [stackexchange, -5 points]

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