[seqfan] Re: "see Mathematica program for definition"
Peter Luschny
peter.luschny at googlemail.com
Mon Oct 24 23:28:02 CEST 2011
>FTAW: I have one real problem with the way Peter has identified
>FTAW: orderings of partitions,
Not sure if I understand your problem. I propose on my page (link given)
"to characterize orderings of integer partitions by a triple
[traverse, increase/decrease, forward/reverse]."
[ VLR , p < q, [1..1] < [n] ] -> "Maple"
[ VLR , p > q, [1..1] > [n] ] -> "Mathematica"
[ VLR*, p < q, [1..1] > [n] ] -> "A. & St."
VLR is the is the preorder traversal of the Fenner-Loizou tree,
VLR* is the same after substitution of a partition by it's conjugate.
p < q means 'increasing parts' and
[1..1] < [n] means the partition [1..1] precedes the partition [n].
I do /not/ use the nomenclature of A036036 nor did I introduce it there.
"Abramowitz and Stegun" -> graded reflected colexicographic ordering.
"Maple" -> graded reflected lexicographic ordering.
"Mathematica" -> graded reverse lexicographic ordering.
The reason is, as I wrote (link given):
"Perhaps this (i.e. the description by the above triples) is the most
succinct way to express the sometimes confusing interplay of the
relations involved; in any case less intimidating than something like
'graded reverse reflected colexicographic order ..' yet more informative
than something profane like "A. & St." order."
>FTAW: The average user of the OEIS, seeing "graded colexigraphic ordering",
>FTAW: is not going to know what this means.
Exactly what I said.
>FTAW: So what should these be named?
[ VLR , p < q, [1..1] < [n] ] <- "Maple"
[ VLR , p > q, [1..1] > [n] ] <- "Mathematica"
[ VLR*, p < q, [1..1] > [n] ] <- "A. & St."
Peter
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