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  • NUMERICAL SEMIGROUPS FROM RATIONAL MATRICES II: MATRICIAL DIMENSION DOES NOT EXCEED MULTIPLICITY

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  • ARSH CHHABRA, STEPHAN RAMON GARCIA, CHRISTOPHER O’NEILL
  • Journal:
    Bulletin of the Australian Mathematical Society , First View
    Published online by Cambridge University Press:
    12 December 2024, pp. 1-8
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  • We continue our study of exponent semigroups of rational matrices. Our main result is that the matricial dimension of a numerical semigroup is at most its multiplicity (the least generator), greatly improving upon the previous upper bound (the conductor). For many numerical semigroups, including all symmetric numerical semigroups, our upper bound is tight. Our construction uses combinatorially structured matrices and is parametrised by Kunz coordinates, which are central to enumerative problems in the study of numerical semigroups.