کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4597504 | 1336219 | 2009 | 6 صفحه PDF | دانلود رایگان |

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).
Journal: Journal of Pure and Applied Algebra - Volume 213, Issue 8, August 2009, Pages 1558–1563