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Spanning trees and continued fractions

Published 27 Nov 2024 in math.CO and math.NT | (2411.18782v2)

Abstract: We prove the exponential growth of the cardinality of the set of numbers of spanning trees in simple (and planar) graphs on $n$ vertices, answering a question of Sedl\'a\v{c}ek from 1969. The proof uses a connection with continued fractions, ``thin orbits,'' and Zaremba's conjecture.

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