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PreprintCC BY 4.0arXiv

Enumeration of zero-sum subsequences: A proof of Bialostocki-Lotspeich conjecture

  • Guoqing Wang
  • Xiangneng Zeng
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Abstract

Let Cn be a cyclic group of order n≥ 2, and let S=g1·…· gℓ be a sequence over Cn, with repetitions allowed. We denote by N0n(S) the number of subsets I⊆[1,ℓ] with |I|=n and ∑i∈ Igi=0. A conjecture proposed by Bialostocki and Lotspeich in 1992 states that N0n(S)≥ binom⌊ |S|/2⌋n+ binom⌈ |S|/2⌉n. Several partial results toward this conjecture are known. In this paper, we prove this conjecture completely.

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Cite

BibTeXRIS
BibTeX
@misc{wang2026enumeration,
  title = {{Enumeration of zero-sum subsequences: A proof of Bialostocki-Lotspeich conjecture}},
  author = {Guoqing Wang and Xiangneng Zeng},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.37125},
  eprint = {2610.37125},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.37125},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Enumeration of zero-sum subsequences: A proof of Bialostocki-Lotspeich conjecture
AU  - Guoqing Wang
AU  - Xiangneng Zeng
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.37125
UR  - https://arxiv.org/abs/2610.37125
AB  - Let C_n be a cyclic group of order n≥ 2, and let S=g_1·…· g_ℓ be a sequence over C_n, with repetitions allowed. We denote by N_0^n(S) the number of subsets I⊆[1,ℓ] with |I|=n and ∑_i∈ Ig_i=0. A conjecture proposed by Bialostocki and Lotspeich in 1992 states that N_0^n(S)≥ binom⌊ |S|/2⌋n+ binom⌈ |S|/2⌉n. Several partial results toward this conjecture are known. In this paper, we prove this conjecture completely.
ER  -