Abstract A real polynomial p of degree n is called a Morse polynomial if its derivative has n?1 pairwise distinct real roots and values of p at these roots (critical values) are also pairwise distinct. The plot of such a polynomial is called a “snake.” By enumerating critical points and critical values in increasing order, we construct a permutation a1, . . . , an?1, where ai is the number of the polynomial’s value at the ith critical point. This permutation is called the passport of the snake (polynomial). In this work, for Morse polynomials of degree 5 and 6, we describe the partition of the coefficient space into domains of constant passport.
展开▼
机译：摘要 如果一个 n 阶的实多项式 p 的导数具有 n？1 个成对不同的实根，并且这些根处的 p 值（临界值）也是成对不同的，则称为莫尔斯多项式。这种多项式的图称为“蛇”。通过按递增顺序枚举临界点和临界值，我们构造了一个排列 a1， . . . ， an？1，其中 ai 是多项式在第 i 个临界点处的值的个数。这种排列称为蛇的护照（多项式）。在这项工作中，对于 5 次和 6 次的莫尔斯多项式，我们描述了系数空间划分为常数护照域的过程。
展开▼
