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What factors constrain the arrangement of the multiple fields of a place cell? By modeling place cells as perceptrons that act on multiscale periodic grid-cell inputs, we analytically enumerate a place cell's repertoire - how many field arrangements it can realize without external cues while its grid inputs are unique; and derive its capacity - the spatial range over which it can achieve any field arrangement. We show that the repertoire is very large and relatively noise-robust. However, thedoi:10.7554/elife.62702 pmid:34028354 pmcid:PMC8294848 fatcat:fu7ajpzv4vfc7jwwejfoavepie