[seqfan] Re: A002088,A015614,A018805 errata

[Olivier Gerard]

Michael Somos wrote:
>
>I distinguish Sets, Multisets, and Lists. For a set, neither order nor
>multiplicity matter. For a multiset, multiplicity matters, order doesn't.
>For a list, both order and multiplicity matter. There is no commonly used
>term for a collection in which order matters, but multiplicity doesn't.
>Another term for List is Vector. Terminology can be confusing at times.
>
And even the word "matter" can be ambiguous. I would say that in sets
identical elements collapse. For the lacking word what about a
"Set"  for a (Single representative) set
"Met"  for a multiset ?
"Sist"  for a set-like list ?
"Mist"  for a Mathematical list ?

it would make a very regular quatuor

>So, Olivier in A015614 considered "pair" to mean "a set with 2 members".
>Also, in A002088 he considered "ordered pair" to mean "a multiset of size 2".
>However, these are not the common meanings. It would be very good to have
>a uniform set of terminology to use for sequence entries.
>

I agree that I have not always been consistent with terminology,
and I am happy you spotted these.  I apologize to Neil for that.
It certainly comes from the interaction with programming languages.

[..]

The solution you propose (use mathematical notation for set definition)
is certainly the most accurate unless one develop an online glossary
for the EIS (where these definitions would be given among other things).


>
>By the way, notice another inconsistency. The origin for A002088 is 0, but for
>the other sequences it is 1. I don't know any reason for the difference.
>

I have just added an interpretation in terms of (multi)-sets to A002088, the
original is in term of the totient function. It may explain the
difference.