Combinatorial identities for binary necklaces from exact ray-splitting trace formulae
R. Bl\"umel, Yu. Dabaghian
TL;DR
This paper derives new combinatorial identities for binary necklaces using an exact trace formula from a one-dimensional ray-splitting system, linking spectral theory with combinatorics.
Contribution
It introduces a novel approach connecting trace formulas with combinatorial identities for cyclic binary sequences.
Findings
Derived new combinatorial identities for binary necklaces.
Linked spectral trace formulas with combinatorial structures.
Provided mathematical tools for analyzing binary cyclic sequences.
Abstract
Based on an exact trace formula for a one-dimensional ray-splitting system, we derive novel combinatorial identities for cyclic binary sequences (P\'olya necklaces).
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