Kosta, D. and Thoma, A. (2020) Unboundedness of Markov complexity of monomial curves in An for n ≥ 4. Journal of Pure and Applied Algebra, 224(6), 106249. (doi: 10.1016/j.jpaa.2019.106249)
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Abstract
Computing the complexity of Markov bases is an extremely challenging problem; no formula is known in general and there are very few classes of toric ideals for which the Markov complexity has been computed. A monomial curve C in A3 has Markov complexity m(C) two or three. Two if the monomial curve is complete intersection and three otherwise. Our main result shows that there is no d ∈ N such that m(C) ≤ d for all monomial curves C in . The same result is true even if we restrict to complete intersections. We extend this result to all monomial curves in An, where n ≥ 4.
Item Type: | Articles |
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Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Kosta, Dr Dimitra |
Authors: | Kosta, D., and Thoma, A. |
College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
Journal Name: | Journal of Pure and Applied Algebra |
Publisher: | Elsevier |
ISSN: | 0022-4049 |
ISSN (Online): | 1873-1376 |
Published Online: | 21 October 2019 |
Copyright Holders: | Copyright © 2019 Elsevier |
First Published: | First published in Journal of Pure and Applied Algebra 224(6):106249 |
Publisher Policy: | Reproduced in accordance with the copyright policy of the publisher |
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