Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Large $\{0, 1, \ldots, t\}$-Cliques in Dual Polar Graphs   We investigate $\{0, 1, \ldots, t \}$-cliques of generators on dual polar
graphs of finite classical polar spaces of rank $d$. These cliques are also
known as Erd\H{o}s-Ko-Rado sets in polar spaces of generators with pairwise
intersections in at most codimension $t$. Our main result is that we classify
all such cliques of maximum size for $t \leq \sqrt{8d/5}-2$ if $q \geq 3$, and
$t \leq \sqrt{8d/9}-2$ if $q = 2$. We have the following byproducts. (a) For $q
\geq 3$ we provide estimates of Hoffman's bound on these $\{0, 1, \ldots, t
\}$-cliques for all $t$. (b) For $q \geq 3$ we determine the largest, second
largest, and smallest eigenvalue of the graphs which have the generators of a
polar space as vertices and where two generators are adjacent if and only if
they meet in codimension at least $t+1$. Furthermore, we provide nice explicit
formulas for all eigenvalues of these graphs. (c) We provide upper bounds on
the size of the second largest maximal $\{0, 1, \ldots, t \}$-cliques for some
$t$.

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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con