What does this research mean for the field?

An explicit infinite family of symmetric numerical semigroups carries nonprincipal rigid ideals that serve as counterexamples to the Huneke-Wiegand conjecture, with the minimal counterexample occurring at a Frobenius number of 181. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.CHALLENGES_CONSENSUS.

What question did this study set out to answer?

Establish the minimality of the first counterexample to the Huneke-Wiegand conjecture for two-generated monomial ideals over symmetric numerical semigroup rings and construct an infinite family with complete homological characterization.

August 31, 2026Open Access

Frobenius minimality, minimum-layer uniqueness, and an infinite family of Huneke-Wiegand counterexamples

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Authors

FSFelipe Santibañez-LealOpen University of Cyprus

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Implication

Theoretical and computational analysis reveals an infinite family of counterexamples to the Huneke-Wiegand conjecture in numerical semigroup rings, demonstrating minimal Frobenius boundaries.

Key Points

Establish the minimality of the first counterexample to the Huneke-Wiegand conjecture for two-generated monomial ideals over symmetric numerical semigroup rings and construct an infinite family with complete homological characterization.
Conducted theorem-tree enumeration and verified 1,156 DRAT proofs using a selector CNF across odd Frobenius numbers through 181.
Constructed a parameterized family of symmetric numerical semigroups for all integers p ≥ 4 using seven exact interval-sum identities.
Computed conductor reductions, tangent-cone cohomology, and multigraded Betti numbers via Presburger verification, colon ideals, and minimal mapping cones.
Proved that the least Frobenius number admitting a counterexample is 181, attained uniquely by Pham's semigroup at shift 14.
Constructed an infinite counterexample family with multiplicity 24p and Frobenius number 78p-1, showing tangent cones are Buchsbaum with invariant p and depth zero.
Demonstrated characteristic dependence in the special fiber resolution, where the Betti number beta_(5,(7,87)) equals 4 over GF(2) and 3 over GF(3).

Cite This Study

Felipe Santibañez-Leal (2026) studied this question.

synapsesocial.com/papers/6a95427bf20e493292a74c63 https://doi.org/10.5281/zenodo.22177072

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Implication

Theoretical and computational analysis reveals an infinite family of counterexamples to the Huneke-Wiegand conjecture in numerical semigroup rings, demonstrating minimal Frobenius boundaries.

Frobenius minimality, minimum-layer uniqueness, and an infinite family of Huneke-Wiegand counterexamples

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Implication

Key Points

Cite This Study

Frobenius minimality, minimum-layer uniqueness, and an infinite family of Huneke-Wiegand counterexamples

Discussion

Member takes

Implication

Key Points

Cite This Study

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