{
  "annotation_id": "8229d38c-d097-4ce7-b2c8-cff7e47e8a59",
  "date_created": "2026-02-17T05:53:11.558000Z",
  "date_modified": "2026-02-17T05:53:11.558000Z",
  "file_hash": "ec96f345d86ab69e7a62747aa058215e0171f4446148b68946bda38426b3989d",
  "private": false,
  "record": {
    "abstract": "Let a, k, h, c be positive integers and d a non zero integer. Recall that a numerical generalized almost arithmetic semigroup S is a semigroup minimally generated by relatively prime positive integers a, ha + d, ha + 2d, . . . , ha + kd, c, that is its embedding dimension is k + 2. In a previous work, the authors described the Ap{\\\u0027e}ry set and a Gr{\\\"o}bner basis of the ideal defining S under one technical assumption, the complete version will be published in a forthcoming paper. In this paper we continue with this assumption and we describe the Pseudo Frobenius set. As a consequence we give a complete description of S when it is symmetric or almost symmetric as well as generalize and extend the previous results of Ignacio Garc{\\\u0027i}a-Marco, J. L. Ram{\\\u0027i}rez Alfons{\\\u0027i}n and O. J. R{{\\o}}dseth; we also find a quadratic formula for its Frobenius number that generalizes some results of J.C. Rosales, and P.A. Garc{\\\u0027i}a-S{\\\u0027a}nchez. Moreover, for given numbers a, d, k, h, c, a simple algorithm allows us to determine if S is almost symmetric or not and furthermore to find its type and Frobenius number.",
    "arxiv_id": "2601.07467",
    "authors": [
      "Marcel Morales",
      "Nguyen Thi Dung"
    ],
    "categories": [
      "math.AC",
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Frobenius Number Of Almost Symmetric Numerical Generalized Almost Arithmetic Semigroups",
    "url": "https://arxiv.org/abs/2601.07467",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "edf14a56-fea0-434a-ae60-42897cece711",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}