Rustem Takhanov

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20242026

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cs.IT2026

Structure of kissing arrangements in $R^{12}$ and a place for the $841$ st sphere

Rustem Takhanov, Zhenisbek Assylbekov, Stanislav Yun

Most currently known kissing arrangements of size $840$ in $R^{12}$ share a common structure. They consist of $60$ vectors supported on $R^{6} \times {0}$ , an…

cs.IT2026

Classification of independent sets in signed Johnson graphs and applications to kissing arrangements

Rustem Takhanov, Stanislav Yun

Johnson graph are a family of graphs that play an important role in the theory of constant-weight codes, extremal combinatorics, and combinatorial geometry. We study signed analogu…

Structure of kissing arrangements in R12 and a place for the 841st sphere

Classification of independent sets in signed Johnson graphs and applications to kissing arrangements

Structure of kissing arrangements in $R^{12}$ and a place for the $841$ st sphere