The Strong Factorial Conjecture
The Strong Factorial Conjecture
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DOI：
10.1016/j.jalgebra.2013.09.011
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发表时间：
2013-04
期刊：
影响因子：
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通讯作者：
E. Edo;A. Essen
中科院分区：
文献类型：
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作者：
E. Edo;A. Essen
本文给出了阶乘猜想[8]与Furter的刚性猜想[13]之间的一个意想不到的联系。m维阶乘猜想断言，如果C上m个变量Xi的多项式f使得L（fk）= 0，对于所有k <$1，则f= 0，其中L是从C [X1，...，Xm]到C的C-线性映射，定义为L（X1 l1 <$Xmlm）= l1！快！刚性猜想断言，一个一元多项式映射a（X）的复系数至多为m+ 1，使得a（X）<$X mod X 2等于X，如果a（X）的形式逆（对于复合）的m个连续系数为零。
In this paper, we present an unexpected link between the Factorial Conjecture [8] and Furterʼs Rigidity Conjecture [13]. The Factorial Conjecture in dimension m asserts that if a polynomial f in m variables X i over C is such that L (f k)= 0 for all k⩾ 1, then f= 0, where L is the C-linear map from C [X 1,…, X m] to C defined by L (X 1 l 1⋯ X m l m)= l 1!⋯ l m!. The Rigidity Conjecture asserts that a univariate polynomial map a (X) with complex coefficients of degree at most m+ 1 such that a (X)≡ X mod X 2, is equal to X if m consecutive coefficients of the formal inverse (for the composition) of a (X) are zero.