Fooling-sets and rank
نویسندگان
چکیده
ABSTRACT. An n×n matrix M is called a fooling-set matrix of size n if its diagonal entries are nonzero and Mk,lMl,k = 0 for every k 6= l. Dietzfelbinger, Hromkovič, and Schnitger (1996) showed that n ≤ (rkM)2 , regardless of over which field the rank is computed, and asked whether the exponent on rkM can be improved. We settle this question. In characteristic zero, we construct an infinite family of rational fooling-set matrices with size n = (rkM+1 2 )
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ورودعنوان ژورنال:
- Eur. J. Comb.
دوره 48 شماره
صفحات -
تاریخ انتشار 2015