Use modular and algebraic methods to improve Shannon-capacity bounds

Determine whether the modular and algebraic approaches developed for independence polynomials of strong products of cycles yield new or sharper bounds on the Shannon capacities of cycles.

Background

The paper connects independence polynomials of strong products of cycles with graph-theoretic and information-theoretic questions. In particular, it notes an apparent inverse relationship between the simplicity of Shannon capacity and the complexity of the associated root structure.

The authors leave unresolved whether the modular-collapse and algebraic methods developed in the paper can produce new or improved bounds for the Shannon capacity of cycles.

References

Shannon Capacity Connections: Investigating the apparent inverse relationship between simplicity of Shannon capacity and complexity of root structure. Do the modular and algebraic approaches introduced here yield new or sharper bounds on the Shannon capacity of cycles?

— Algebraic and Combinatorial Stability of Independence Polynomials in Iterated Strong Products of Cycles  (2503.07910 - Hildebrant, 10 Mar 2025) in Section 6, “Future Directions,” item 4

Do the modular and algebraic approaches introduced here yield new or sharper bounds on the Shannon capacity of cycles?

— Algebraic and Combinatorial Stability of Independence Polynomials in Iterated Strong Products of Cycles  (2503.07910 - Hildebrant, 10 Mar 2025) in Section 6, “Future Directions” (labelled sec:future-research)