4 research outputs found
Proof of the Kresch-Tamvakis Conjecture
In this paper we resolve a conjecture of Kresch and Tamvakis. Our result is
the following.
Theorem: For any positive integer and any integers , 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
The girth, odd girth, distance function, and diameter of generalized Johnson graphs
For any non-negative integers , the {\em generalized Johnson
graph}, , is the undirected simple graph whose vertices are the
-subsets of a -set, and where any two vertices and are adjacent
whenever . In this article, we derive formulas for the girth,
odd girth, distance function, and diameter of
On the Girth and Diameter of Generalized Johnson Graphs
Let v \u3e k \u3e i be non-negative integers. The generalized Johnson graph, J(v,k,i), is the graph whose vertices are the k-subsets of a v-set, where vertices A and B are adjacent whenever |A∩B|= i. In this article, we derive general formulas for the girth and diameter of J(v,k,i). Additionally, we provide a formula for the distance between any two vertices A and B in terms of the cardinality of their intersection