User talk:Charles R Greathouse IV/Properties

Arithmetic sequences and eventually...

Arithmetic sequences (linear sequences) would go between constant sequences and polynomial sequences.

Earithmetic sequences (Elinear sequences) would go between Econstant sequences and Epolynomial sequences.

— Daniel Forgues 05:16, 22 July 2012 (UTC)

On a light note, perhaps the empty sequence would go above constant sequences... — Daniel Forgues 05:16, 22 July 2012 (UTC)

Certainly I could insert specific polynomial degrees into the chart: quadratic polynomials are polynomials, linear polynomials are polynomials, etc. Similarly I could include some of the properties I mention in the list but don't have charted at the moment: multiplicity sequences, quasi-multiplicative sequences, etc. I have a chart which adds some of this information but it's even larger and harder to read than the present one (and, IMO, the addition of multiplicity sequences makes the shape of the chart much less pleasing). Perhaps there is a better way to present the information?

On the empty sequence: So far I've managed to keep myself from adding single sequences to the chart. My inclination (which I have thus far resisted) was to add A000012 since it implies both cmult and constant and thus everything else on the chart.

As a terminological note, I very much prefer "linear sequences" to "arithmetic sequences" as the latter makes me think of arithmetic functions in which "arithmetic" means something other than "arithmetic progression".

Charles R Greathouse IV 07:08, 22 July 2012 (UTC)

I didn't know about multiplicity sequences! Yes, it is analogous to [strong] divisibility sequences, but with lcm instead of gcd! I found this paper

Piotr Zarzycki, ON MULTIPLICITY SEQUENCES, 1995.

— Daniel Forgues 08:48, 22 July 2012 (UTC)

I also do very much prefer "linear sequences" to "arithmetic sequences." — Daniel Forgues 09:28, 22 July 2012 (UTC)

Yes, that's where I learned the term. The paper is cited (reference 3). Charles R Greathouse IV 17:34, 22 July 2012 (UTC)