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This paper introduces the concept of necklace binomial coefficients motivatedby the enumeration of a special type of sequences. Several properties of thesecoefficients are described, including a connection between their roots and anelliptic curve. Further links are given to a physical model from quantummechanical supersymmetry as well as properties of alkane molecules inchemistry.

Broken bracelets, Molien series, paraffin wax and an elliptic curve of conductor 48