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A foundational component of developing combinatorial fluency is the ability to identify and quantify structure in the set of outcomes being counted. Yet, there are often multiple ways to represent the outcomes, and not all representations equally elucidate structure. This paper applies a semiotic lens to combinatorial reasoning, with an emphasis on characterizing the relationship between sets of outcomes, their representations (both institutional and not), and numerical solutions. In particular, combinatorial reasoning is framed as transformations between sufficiently proximal representations that preserve a narrative meaning. I demonstrate how this framing explains difficulties encountered by undergraduate students, and how it can be used to understand the role of auxiliary representations students create as they solve counting problems.