On nilpotence indices of sign patterns
Published in Commun. Korean Math. Soc., 2010
The work in this paper was motivated by Eschenbach and Li, who listed four 4-by-4 sign patterns, conjectured to be nilpotent sign patterns of nilpotence index at least 3. These sign patterns with no zero entries, called full sign patterns, are shown to be potentially nilpotent of nilpotence index 3. We also generalize these sign patterns of order 4 so that we provide classes of n-by-n sign patterns of nilpotence indices at least 3, if they are potentially nilpotent. Furthermore it is shown that if a full sign pattern A of order n has nilpotence index k with 2≤k≤n−1, then sign pattern A has nilpotent realizations of nilpotence indices k, k+1,…,n.
Recommended citation: C. Erickson and I.-J. Kim. ”On nilpotence indices of sign patterns.” Commun. Korean Math. Soc. 25 (2010), No. 1, 11—18.