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Abstract: Hexaflexagons were popularized by the late Martin Gardner in his firstScientific American column in 1956. Oakley and Wisner showed that they can berepresented abstractly by certain recursively defined permutations called pats,and deduced that they are counted by the Catalan numbers. Counting pats bynumber of descents yields the curious identitySum1-2n-2k+1binom{2n-2k+1}{k}binom{2k}{n-k},k=0

n = Cn, where only themiddle third of the summands are nonzero.



Author: David Callan

Source: https://arxiv.org/







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