距离正则图的伪余弦序列
The Pseudo Cosine Sequences of a Distance-Regular Graph
摘要：
设$G$表示距离正则图，其直径为$D\ge 3$，度为$k$，交叉数为$a_i$，$b_i$，$c_i$ .对于$G$的{ \it伪余弦序列}，我们是指实数序列$s_0, s_1, ..., s_D$，使得$s_0=1$和$c_i s_{i-1}+a_i s_i+b_i s_{i+1}=k s_1 s_i$用于$ 0 \le i \le D-1$。令$s_0, s_1,..., s_D$和$p_0, p_1, ..., p_D$表示$G$的伪余弦序列。只要$s_0 p_0, s_1 p_1, ..., s_D p_D$是$G$的伪余弦序列，我们就说这对序列是{ \it紧}的。本文确定了$G$的伪余弦序列的所有紧偶。
英文摘要：
Let $G$ denote a distance-regular graph with diameter $D\ge 3$, valency $k$, and intersection numbers $a_i$, $b_i$, $c_i$. By a {\it pseudo cosine sequence} of $G$ we mean a sequence of real numbers $s_0, s_1, ..., s_D$ such that $s_0=1$ and $c_i s_{i-1}+a_i s_i+b_i s_{i+1}=k s_1 s_i$ for $ 0 \le i \le D-1$. Let $s_0, s_1,..., s_D$ and $p_0, p_1, ..., p_D$ denote pseudo cosine sequences of $G$. We say this pair of sequences is {\it tight} whenever $s_0 p_0, s_1 p_1, ..., s_D p_D$ is a pseudo cosine sequence of $G$. In this paper, we determine all the tight pairs of pseudo cosine sequences of $G$.
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