A comma operator in laconic notations

The comma symbol `$,$' is ubiquitously used in mathematics, logic, and computer science to separate elements of lists, tuples, arguments, or conjunctions. Yet it has rarely been treated as a formal operator with its own algebraic structure. In this paper we define the \textit{comma operator} as a primitive binary operation that constructs ordered sequences, and we develop its algebraic properties within a monoid of sequences. We relate this notion to the comma operator in programming languages and to comma categories in category theory. We then demonstrate genuine notational problems --- the unambiguous compact representation of nested variable-length sums and the multinomial theorem --- that are naturally solved by our comma operator. Finally, we adopt a philosophical and foundational perspective, arguing that the comma operator is as primitive as the logical connectives or quantifiers, and we sketch a minimalist formal language whose only syntactic operations are concatenation (the comma) and set formation. This work continues the tradition of \textit{laconic} notation in mathematics and philosophy. \\ ( \textit{To be revised: Comments are welcomed! :)} )

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