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On the degrees of minimal generators of homogeneous ideals in the exterior algebra
Moreno-Socías, G., Laboratoire GAGE, École Polytechnique, F-91128 Palaiseau Cedex, France.
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
2001 (English)In: Communications in Algebra, ISSN 0092-7872, Vol. 29, no 11, 5155-5170 p.Article in journal (Refereed) Published
Abstract [en]

We study how homogeneous ideals in the exterior algebra ? V over a finite-dimensional vector space V are minimally generated. In particular, we solve the following problems: Starting with an element pv of degree v, what is the maximum length l of a sequence pv, . . . , pv+l-l, with degpi = i, and such that pi is not in the ideal generated by pl, . . . , pi-l? What is the maximal possible number of minimal generators of degree d of a homogeneous ideal which does not contain all elements of degree d + 1? Our main tool is the Kruskal-Katona theorem.

Place, publisher, year, edition, pages
2001. Vol. 29, no 11, 5155-5170 p.
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-47218DOI: 10.1081/AGB-100106808OAI: diva2:268114
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2011-01-13

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