关于Cayley分解的一个注解

A note on Cayley factorization

对于任意长度r≥3的齐次括号多项式,一定存在括号单项式,使之Cayley可分解的结论已被证明,然而却没有给出任何有关该单项式的性质,为此通过几个反例证明了这种括号单项式具有即使是次数最低的也不一定是唯一的性质.

Sturmfels and Whiteley proved that for any homogeneous bracket polynomial of length r≥3,there must be a bracket monomial,which made the polynomial be Cayley factored after multiplied it,but they did not give any property of this monomial.In this text,it is proved that even the monomial of the least degree is not unique.