Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 44 min ago
PreprintCC BY 4.0arXiv

The type and cardinality of minimal presentations of numerical semigroups with embedding dimension four

  • Kazimierz Chomicz
Open at sourcePDFDOICite

Abstract

For a numerical semigroup S with embedding dimension four, we study the relationship between its type t(S) and the cardinality of its minimal presentations η(S). Using an approach based on the geometry of the Apéry set, we prove that 4t(S) + 5 ≥ η(S) ≥ t(S)−11. This resolves a problem of Moscariello and Sammartano asking whether t(S) is bounded by a function of η(S), and improves the previously known bound 9t(S) + 4 ≥ η(S) due to Bresinsky.

Related

  1. A criterion for determinantal presentations of numerical semigroup rings
    Satoshi Murai, Kou Takahashi
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. Periodic Tilings of Cardinality Twice a Prime or Nine in Arbitrary Dimension
    Hu Tan, Ying Zhang
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsarXiv
  3. Power sums of critical points of gap polynomials for symmetric and pseudo-symmetric numerical semigroups
    Pavel Grinfeld
    arXivPreprintCC0Full textAlgebra & number theoryarXiv
  4. Telescopic Structure of Numerical Semigroups Generated by Unsigned Stirling Numbers of the First Kind
    Takao Komatsu, Kyunghwan Song
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  5. Goldman primes and higher cyclic presentations for the small finitistic dimension
    Xiaolei Zhang, Hwankoo Kim
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{chomicz2026type,
  title = {{The type and cardinality of minimal presentations of numerical semigroups with embedding dimension four}},
  author = {Kazimierz Chomicz},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.04000},
  eprint = {2609.04000},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.04000},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The type and cardinality of minimal presentations of numerical semigroups with embedding dimension four
AU  - Kazimierz Chomicz
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.04000
UR  - https://arxiv.org/abs/2609.04000
AB  - For a numerical semigroup S with embedding dimension four, we study the relationship between its type t(S) and the cardinality of its minimal presentations η(S). Using an approach based on the geometry of the Apéry set, we prove that 4t(S) + 5 ≥ η(S) ≥ t(S)−11. This resolves a problem of Moscariello and Sammartano asking whether t(S) is bounded by a function of η(S), and improves the previously known bound 9t(S) + 4 ≥ η(S) due to Bresinsky.
ER  -