2 problems

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Conjecture on the minimum alphabet size for a given nesting index
Minimum-alphabet-size conjecture. The number of letters needed to construct a double occurrence word with nesting index $n$ is
Conjectureopendouble-occurrence-words graph-theoryarXiv posted 2 days ago
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Characterization of assembly graphs with genus range {0,1}
Genus-range characterization. Any DOW whose corresponding graph has genus range $\{0,1\}$ is obtained from the word
Conjectureopendouble-occurrence-words genus-theory topological-graph-theoryarXiv posted 2 days ago

Conjecture on the minimum alphabet size for a given nesting index