Wikipedia:Reference desk/Archives/Mathematics/2014 December 13

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December 13

Meandric numbers

According to Meander (mathematics), and (sequence A005315 in the OEIS), the third meandic number is eight. Ok, so I can find four distinct meanders, A1 to A4, with 2³ crossings and along with their horizontal reflections, B1 to B4, make the required eight. But wait, some of them, C2 to C4, have a vertical reflection not homomorphic to any of the eight, and along with their horizontal reflections, D2 to D4, make a total of 14. What am I missing? SpinningSpark 11:29, 13 December 2014 (UTC)

The pdf linked in the article gives all 8. The problem is that yours are crossing the line 8 times, not 6. (It's 2n not 2^n, so you should have 6 crossings)Phoenixia1177 (talk) 12:59, 13 December 2014 (UTC)

Ah, thanks. I knew it had to be something simple. Just for the record, I found quite a few more with eight crossings after posting the diagram. SpinningSpark 13:17, 13 December 2014 (UTC)