The fractions $n/q$ and $n/(n-q)$ can be representated by Hirzebruch continued fractions (also called Jung-Hirzebruch CF), the length of each we denote by $s$ and $t$. Is there any bound for $s+t$?
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4$\begingroup$ What's a Hirzebruch continued fraction? $\endgroup$– Gerry MyersonJul 13, 2011 at 11:45
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$\begingroup$ Gerry Myerson, it seems to be like a continued fraction but with minuses instead of pluses; see cems.uvm.edu/~voight/notes/cfrac.pdf page 9. Also called Jung--Hirzebruch CF. $\endgroup$– user9072Jul 13, 2011 at 12:39
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1$\begingroup$ My guess is that $s+t \leq n$, reached for $q=1$. $\endgroup$– Francesco PolizziJul 13, 2011 at 14:02
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1$\begingroup$ @quid, thanks. These would be what I called negative-regular continued fractions in my 1987 paper in Arch. Math. $\endgroup$– Gerry MyersonJul 14, 2011 at 5:28
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$\begingroup$ Correct link to "TORIC SURFACES AND CONTINUED FRACTIONS": math.dartmouth.edu/~jvoight/notes/cfrac.pdf $\endgroup$– Alexey UstinovDec 14, 2013 at 2:55
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