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Positivity and negativity for $h$-bases for $n$ — arXiv:2610.19470

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.19470
License (as archived): CC0-1.0
Archived: 2026-10-15T21:52:40.230Z
SHA-256 of the archived text: d2ed68e7451bd339495a719b2cdd00e1c873d8e54eadfd96a2ef0396baf4e04e
Stable URL of this page: https://metraipolis.com/documento/dc_367beb1dd488

How to cite

Positivity and negativity for $h$-bases for $n$ — arXiv:2610.19470 — arXiv (en), https://arxiv.org/abs/2610.19470 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_367beb1dd488 (Metraipolis archive dc_367beb1dd488, sha256 d2ed68e7451bd339495a719b2cdd00e1c873d8e54eadfd96a2ef0396baf4e04e)

BibTeX

@misc{dc367beb1dd488,
  title = {Positivity and negativity for $h$-bases for $n$ — arXiv:2610.19470},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.19470},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_367beb1dd488; sha256 d2ed68e7451bd339495a719b2cdd00e1c873d8e54eadfd96a2ef0396baf4e04e},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.19470. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

A set $A$ of integers is an $h$-basis for $n$ if every integer in $[0,n] = \{0,1,2,\ldots,n\}$ belongs to the sumset $hA$, that is, can be represented as the sum of exactly $h$ not necessarily distinct elements of $A$. The classical postage stamp problem asks for the largest integer $n_h(k)$ such that $[0,n_h(k)] \subseteq hA$ for some set $A$ of nonnegative integers of size $k+1$. We consider the effect of allowing negative elements. Let $n^{\flat}_h(k)$ be the largest integer such that $[0,n^{\flat}_h(k)] \subseteq hA$ for some set $A$ of integers of size $k+1$ containing at least one negative integer. For $k=2$, we have $n^{\flat}_h(2) < n_h(2)$ if $h$ is odd or $h=4$ and $n^{\flat}_h(2) = n_h(2)$ if $h$ is even and $h \neq 4$. Proofs of these comparison results were autonomously discovered and formally verified in Lean by this https URL }{Aristotle}, a formal reasoning agent developed by this https URL }{Harmonic}. In this paper we give new proofs of these results.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.CO, nuovi lavori del giorno).
Categorie arXiv: Combinatorics (math.CO) ; Number Theory (math.NT).
Pagina del lavoro: https://arxiv.org/abs/2610.19470 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-15T21:37:14.421Z dalla pagina https://arxiv.org/list/math.CO/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).