A Sequence Bounded Above by the Lucas Numbers

Year 2018, Volume: 22 Issue: 6, 1853 - 1856, 01.12.2018

Ali Aydoğdu , Engin Özkan , Aykut Göçer

https://doi.org/10.16984/saufenbilder.443551

Abstract

In this work, we consider the sequence whose n^th 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 n^th Lucas
number L_n is
showed. The relation between the set of h-vectors L(n) and the
set of integer vectors E(n) is given.

Keywords

Cardinality, h-vectors, Hilbert function, Lucas Numbers

References

• [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.