[seqfan] Re: A064736, A217579 and A302350

Antti Karttunen antti.karttunen at gmail.com
Tue Apr 17 12:35:59 CEST 2018


So far,

After insights from Michel Marcus and Peter Munn, we have found several new
general ways to construct these kinds of permutations where a(n) is always
either a divisor or a multiple of a(n+1). (Mostly based on by playing the
"Fermi-Dirac piano", A052330, with optional pre- and/or post-processing
steps).

But there remains a naming question: how to call them?

There are several suggestions:

Pierre Mazet & Eric Saias call them "chain permutations"
(chaîne-permutation) in their paper https://arxiv.org/abs/1803.10073
I assume this comes after the chains of the divisor lattice, as any two
successive terms belong to a common chain.

Then I suggested "divisor-or-multiple permutations", while Peter suggested
"multiplicative walk permutations", but Michel objected to that, although I
preferred it over my first proposal.

I think "divisor-or-multiple permutations" is a bit ambiguous, because it
could also mean permutations where, say, a(n) is either a divisor or
multiple of n.
So then we would need a phrase like "successor-is-divisor-or-multiple
permutations", with an ugly acronym: "SIDOM permutations". No...

So, I'm in favor of "multiplicative walk permutations", what would other
people say?


Best regards,

Antti



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