arXiv subjects
Publications and source records attributed to Taiyo S. Terada.
For any non-negative integers $v > k > i$, the {\em generalized Johnson graph}, $J(v,k,i)$, is the undirected simple graph whose vertices are the $k$-subsets of a $v$-set, and where any two vertices $A$ and $B$ are adjacent whenever $|A \cap B| =i$. In this article, we derive formulas for the girth, odd girth, distance function, and diameter of $J(v,k,i)$.
In this paper we resolve a conjecture of Kresch and Tamvakis. Our result is the following. Theorem: For any positive integer $D$ and any integers $i,j$ $(0\leq i,j \leq D)$, the absolute value of the following hypergeometric series is at most 1: \begin{equation*} {_4F_3} \left[ \begin{array}{c} -i, \; i+1, \; -j, \; j+1 \\ 1, \; D+2, \; -D \end{array} ; 1 \right]. \end{equation*} To prove this theorem, we use the Biedenharn-Elliott identity, the theory of Leonard pairs, and the Perron-Frobenius theorem.