What question did this study set out to answer?

The central aim is to compute the matricial dimensions of numerical semigroups with defined limits on Frobenius number and genus.

April 1, 2026Open Access

Numerical Semigroups From Rational Matrices Iv: Computation of the Matricial Dimensions of Numerical Semigroups With Small Frobenius Number or Genus

Key Points

The central aim is to compute the matricial dimensions of numerical semigroups with defined limits on Frobenius number and genus.
Employed a module-theoretic approach for analysis
Utilized linear programming for computations
Focused on numerical semigroups with Frobenius number ≤ 10 and genus ≤ 6
Computed matricial dimensions for all relevant numerical semigroups
Results exceed previous computation methods' capabilities

Abstract

Abstract We introduce a module-theoretic approach and a linear-programming method to compute the matricial dimensions of numerical semigroups. We compute the matricial dimension of every numerical semigroup with Frobenius number at most 10 or genus at most 6. Many of these evaluations are beyond the scope of previous techniques.

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Cite This Study

CHINN et al. (Tue,) studied this question.

synapsesocial.com/papers/69ccb76c16edfba7beb895c7 https://doi.org/https://doi.org/10.1017/s0004972726101063

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