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Maximal shifts below the Taylor bound — arXiv:2609.32135

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.32135
License (as archived): CC0-1.0
Archived: 2026-10-07T23:29:22.919Z
SHA-256 of the archived text: 1b0ab864997b44aca644ddac3821ee5a165817a6218a84470b5a0d09b0d78652
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How to cite

Maximal shifts below the Taylor bound — arXiv:2609.32135 — arXiv (en), https://arxiv.org/abs/2609.32135 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_ea49c09a13fb (Metraipolis archive dc_ea49c09a13fb, sha256 1b0ab864997b44aca644ddac3821ee5a165817a6218a84470b5a0d09b0d78652)

BibTeX

@misc{dcea49c09a13fb,
  title = {Maximal shifts below the Taylor bound — arXiv:2609.32135},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.32135},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_ea49c09a13fb; sha256 1b0ab864997b44aca644ddac3821ee5a165817a6218a84470b5a0d09b0d78652},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.32135. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Let $I\subseteq S$ be a monomial ideal with minimal generator degrees between $e$ and $d$, where $2\leq e\leq d$. We prove that if $t_a(S/I)<ea$, then $$ t_{a+b}(S/I)\leq t_a(S/I)+ \left\lceil\frac{(2d-1)b}{2}\right\rceil $$ for $a\geq2$, $b\geq0$, and $a+b\leq\operatorname{pd}_S(S/I)$. Consequently, $$ t_{a+b}(S/I)\leq ae+db-1-\left\lfloor\frac b2\right\rfloor. $$ In particular, if $t_2(S/I)<2e$, then $$ t_i(S/I)\leq \left\lceil\frac{(2d-1)i}{2}\right\rceil-2(d-e) $$ for $2\leq i\leq\operatorname{pd}_S(S/I)$. We also obtain a regularity bound and give a quadratic family in which our estimate for the last shift is smaller than every bound obtained from ordinary subadditivity. The constant $2d-1$ is sharp for $d=2$.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-29 in math.CO).
Categorie arXiv: Commutative Algebra (math.AC) ; Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2609.32135 — 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 2026-10-07T23:08:10.883Z dalla pagina https://arxiv.org/catchup/math.CO/2026-09-29?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).