[seqfan] Re: Falling factorials divided by rising factorials
Richard J. Mathar
mathar at mpia-hd.mpg.de
Tue Feb 22 10:16:38 CET 2022
jnthn> Questions:
jnthn> (1) Does asking to sort the terms make sense?
jnthn>
jnthn> (2). Is there a "natural choice" of ordering of the row elements?
jnthn> (3) Is there a *concise* and straight forward way to explain why the
jnthn> elements of the rows will never be well-ordered (see last row of example
jnthn> triangle)?
OEIS is a database about sequences and mathematics. Sequence implies
"ordered/tuples" etc.
If you cannot order them, if they are just sets, there is no place for your data
in the OEIS, because the terms would be non-searchable, non-indexable etc.
A sequence like 1,2,3,4,5,6,7,8 *is* different from 2,1,4,3,6,5,8,7,...
that would be created by swapping pairs of numbers.
E.g., the sequence which are permutations of the integers are all considered
different.
We do have cases (like the partitions ...) where different well-defined
orders exist, and where different variants of essentially the same
concept have been added to the OEIS.
All comments by the editors you're quoting so far are well founded.
RJM
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