# [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
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

```