{
  "annotation_id": "f95d90f7-ef6b-4b69-804d-fc715decee0d",
  "date_created": "2026-02-17T05:53:08.857000Z",
  "date_modified": "2026-02-17T05:53:08.857000Z",
  "file_hash": "fbb251e9b3c0224417067efdb98ac64c3dffe4175be8aa2c4b9dc673b344d136",
  "private": false,
  "record": {
    "abstract": "Levenshtein first introduced the sequence reconstruction problem in $2001$. In the realm of combinatorics, the sequence reconstruction problem is equivalent to determining the value of $N(n,d,t)$, which represents the maximum size of the intersection of two metric balls of radius $t$, given that the distance between their centers is at least $d$ and the sequence length is $n$. In this paper, We present a lower bound on $N(n,3,t)$ for $n\\geq 13$ and $t \\geq 4$. For $t=4$, we prove that this lower bound is tight. This settles an open question posed by Pham, Goyal, and Kiah, confirming that $N(n,3,4)=20n-166$ for all $n \\geq 13$.",
    "arxiv_id": "2601.06503",
    "authors": [
      "Xiang Wang",
      "Weijun Fang",
      "Han Li",
      "Fang-Wei Fu"
    ],
    "categories": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Some New Results on Sequence Reconstruction Problem for Deletion Channels",
    "url": "https://arxiv.org/abs/2601.06503",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "78ce0be6-0ef2-43cc-b9cc-8ab3c846790c",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}