ABSTRACT
By cyclically extending recurrences, we find a hierarchy of hierarchies of identities. The technique employed was developed for finding matching polynomials of cyclically labeled paths. The method is based on trace formulas for matrices acting on the space of symmetric tensors. Borrowing terminology from quantum field theory, the action of operators on this space is called “second quantization.” This chapter's main objective is the recurrence, which is the periodic extension of a given recurrence. “Second quantization” appears in the context of the Symmetric Trace Theorem for a matrix acting on the space of symmetric tensors. Looking at path covers and trellises yields combinatorial models for general linear recurrences. For details on matching and matching polynomials in the combinatorial setting. The use of the multiplicative properties of the second quantization provides a way for deeper analysis in contexts where MacMahon’s theorem is used as a counting or analytic technique.
