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신용수 한국전산응용수학회 2008 Journal of applied mathematics & informatics Vol.26 No.5
Abstract. We find a necessary and sufficient condition that the prime factors of Am +1 and Aⁿ+1 coincide for odd positive integers n > m ≥ 1. Moreover, we also find a necessary and sufficient condition that the set of all prime factors of Am + 1 is a subset of those of Aⁿ + 1 for n > m ≥ 1.
Some example of the union of two linear star-configurations in P2 having generic Hilbert function
신용수 충청수학회 2013 충청수학회지 Vol.26 No.2
In [20] and [22], the author proved that the union of two linear star-configurations in P2 of type t × s with 3≤t≤10and t≤s has generic Hilbert function. In this paper, we prove that the union of two linear star-configurations in P2 of type t × s with 3≤t and (t2)-1≤s has also generic Hilbert function.
On The Hilbert Function of The Union of Two Linear Star-Configurations in P2
신용수 충청수학회 2012 충청수학회지 Vol.25 No.3
t has been proved that the union of two linear star-configura- tions in $\P^2$ of type $t\times s$ for $3\le t \le 9$ and $3\le t\le s$ has generic Hilbert function. We extend the condition to $ t=10$, so that it is true for $3\le t \le 10$, which generalizes the result of \cite{S:1}.