کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4597504 1336219 2009 6 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the Gröbner complexity of matrices
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
On the Gröbner complexity of matrices
چکیده انگلیسی

In this paper we show that if for an integer matrix AA the universal Gröbner basis of the associated toric ideal IAIA coincides with the Graver basis of AA, then the Gröbner complexity u(A)u(A) and the Graver complexity g(A)g(A) of its higher Lawrence liftings agree, too. In fact, if the universal Gröbner basis of IAIA coincides with the Graver basis of AA, then also the more general complexities u(A,B)u(A,B) and g(A,B)g(A,B) agree for arbitrary BB. We conclude that for the matrices A3×3A3×3 and A3×4A3×4, defining the 3×3 and 3×4 transportation problems, we have u(A3×3)=g(A3×3)=9u(A3×3)=g(A3×3)=9 and u(A3×4)=g(A3×4)≥27u(A3×4)=g(A3×4)≥27. Moreover, we prove that u(Aa,b)=g(Aa,b)=2(a+b)/gcd(a,b)u(Aa,b)=g(Aa,b)=2(a+b)/gcd(a,b) for positive integers a,ba,b and Aa,b=(11110aba+b).

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Pure and Applied Algebra - Volume 213, Issue 8, August 2009, Pages 1558–1563
نویسندگان
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