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Journals / Sakarya University Journal of Science / 2018 / Cilt: 22 Sayı: 6

A Sequence Bounded Above by the Lucas Numbers

Ali AYDOĞDU
Engin ÖZKAN
Aykut GÖÇER
Pages
1853–1856
Publication Date
2018-12-01
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The relation between the set of h-vectors L(n) and the set of integer vectors E(n) is given.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this work, we consider the sequence whose nth term is the number of h-vectors of length n.
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Key Findings & Data:For, n >=2, the cardinality of E(n) is the nth Lucas number Ln is showed.
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Conclusion & Impact:The relation between the set of h-vectors L(n) and the set of integer vectors E(n) is given.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Cardinality · h-vectors · Hilbert function

Abstract

In this work, we consider the sequence whose nth term is the number of h-vectors of length n. The set of integer vectors E(n) is introduced. For, n >=2, the cardinality of E(n) is the nth Lucas number Ln is showed. The relation between the set of h-vectors L(n) and the set of integer vectors E(n) is given.

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Cite This Article

AYDOĞDU, A., ÖZKAN, E., GÖÇER, A. (2018). A Sequence Bounded Above by the Lucas Numbers. Sakarya University Journal of Science, Cilt: 22 Sayı: 6, 1853–1856. https://ajindex.com/articles/942111

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References (4)

  1. W. Bruns and J. Herzog, “Cohen-Macaulay Rings, in: Cambridge Studies in Advanced Mathematics, vol 39,” Cambridge University Press, Cambridge, 1993
  2. T. Enkosky and B. Stone, “Sequence defined by h-vectors,” Eprint arXiv:1308.4945
  3. T. Enkosky, B. Stone, “A sequence defined by M-sequences,” Discrete Mathematics, vol. 333, pp. 35-38, 2014
  4. E. Ozkan, A. Geçer and İ. Altun, “A new sequence realizing Lucas numbers and the Lucas Bound,” Electronic Journal of Mathematical Analysis and Applications, vol. 5, no. 1, 148-154, 2017.