A Burnside-based enumeration formula, Theorem 4, counts unitary invariant tensor contractions built from fields of multiple orders, recovers known fixed-order counts as a special case, and generates new integer sequences.
Combinatorial Representation Theory
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We attempt to survey the field of combinatorial representation theory, describe the main results and main questions and give an update of its current status. We give a personal viewpoint on the field, while remaining aware that there is much important and beautiful work that we have not been able to mention.
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Multiple-Order Tensor Field Theory: Enumeration of unitary invariant observables
A Burnside-based enumeration formula, Theorem 4, counts unitary invariant tensor contractions built from fields of multiple orders, recovers known fixed-order counts as a special case, and generates new integer sequences.