Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Using symbolic computation to prove nonexistence of distance-regular
  graphs   A package for the Sage computer algebra system is developed for checking
feasibility of a given intersection array for a distance-regular graph. We use
this tool to show that there is no distance-regular graph with intersection
array $\{(2r+1)(4r+1)(4t-1), 8r(4rt-r+2t), (r+t)(4r+1); 1, (r+t)(4r+1),
4r(2r+1)(4t-1)\}$ ($r, t \ge 1$), $\{135, 128, 16; 1, 16, 120\}$, $\{234, 165,
12; 1, 30, 198\}$ or $\{55, 54, 50, 35, 10; 1, 5, 20, 45, 55\}$. In all cases,
the proofs rely on equality in the Krein condition, from which triple
intersection numbers are determined. Further combinatorial arguments are then
used to derive nonexistence.

1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga