A DEGREE BOUND FOR THE GRAVER BASIS OF NON-SATURATED LATTICES

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SABZROU HOSSEIN

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ISSN: 2588-4824

Journal Paper

Paper Information

Journal: BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY Year:2013 | Volume:39 | Issue:5 Page(s): 893-901

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Title

A DEGREE BOUND FOR THE GRAVER BASIS OF NON-SATURATED LATTICES

Author(s)

SABZROU HOSSEIN | Issue Writer Certificate

Keywords

NON-SATURATED LATTICES

GRAVER BASES

Abstract

Let L be a lattice in Zn of dimension m. We prove that the total degree of any Graver element of L is not greater than m (n-m+1) MD, where the integer M is defined by the set of circuits of L, and the integer D is defined by the saturation of L. The case M=1 occurs precisely when L is saturated, and in this case the bound is a reformulation of a well-known bound given by several authors. As a corollary, we show that the Castelnuovo-Mumford regularity of the corresponding lattice ideal IL is not greater than 1/2m (n-1) (n-m+1) MD.

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APA: Copy

SABZROU, HOSSEIN. (2013). A DEGREE BOUND FOR THE GRAVER BASIS OF NON-SATURATED LATTICES. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 39(5), 893-901. SID. https://sid.ir/paper/613574/en

Vancouver: Copy

SABZROU HOSSEIN. A DEGREE BOUND FOR THE GRAVER BASIS OF NON-SATURATED LATTICES. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY[Internet]. 2013;39(5):893-901. Available from: https://sid.ir/paper/613574/en

IEEE: Copy

HOSSEIN SABZROU, “A DEGREE BOUND FOR THE GRAVER BASIS OF NON-SATURATED LATTICES,” BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, vol. 39, no. 5, pp. 893–901, 2013, [Online]. Available: https://sid.ir/paper/613574/en

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