Algebraic Theory of Locally Nilpotent Derivations

Abstract

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Rational constants of cyclotomic derivations

“…Then I 1 = {0, 1, 2, 3, 4, 5}, I 2 = {1, 3} are the 12-sets of type [2,3], and I 1 = {0, 1, 2, 3}, I 2 = {1, 2, 4, 5} are the 12-sets of type [3,2]. Now we calculate the cardinality of the sets I 1 , .…”

“…Let n = 12 = 2 2 3 and consider the type [2,3]. In this case we have: s = 2, p 1 = 2, p 2 = 3, n 1 = 6, n 2 = 4, I 1 = {0, 1, 2, 3, 4, 5} and I 2 = {1, 3}.…”

“…In this case we have: s = 2, p 1 = 2, p 2 = 3, n 1 = 6, n 2 = 4, I 1 = {0, 1, 2, 3, 4, 5} and I 2 = {1, 3}. The 12-standard set A of type [2,3] is the set of the following 8 sequences: Observe that m(2, 1) + m(2, 3) + m(2, 5) = m(3, 1) + m(3, 3). Hence, the set A is not linearly independent over Z.…”

“…Hence, the set A is not linearly independent over Z. This means, that 12 is not a special number of type [2,3]. Now consider n = 12 and the type [3,2].…”

“…In this case p 1 = 3, p 2 = 2, n 1 = 4, n 2 = 6, I 1 = {0, 1, 2, 3} and I 2 = {1, 2, 2, 5}. The 12-standard set A of type [3,2] is in this case the set of the following 8 sequences: It is easy to check that in this case the set A is linearly independent over Z. Thus, 12 is a special number of type [3,2], and 12 is not a special number of type [2,3].…”