I would have guessed "sublinear" but wikipedia doesn't mention what you suggest below: http://en.wikipedia.org/wiki/Sublinear_function Btw. for me these sequences are "inversion tables" of permutations: there are n! such sequences of length n. * Marc LeBrun <mlb@well.com> [Apr 09. 2011 21:19]:
I¹ve been calling an integer sequence X0, X1, X2,... ³gradual² when 0 <= Xn <= n.
I was wondering, is a ³standard² (or better) name for this property?
Obviously the gradual sequences are closed under min, max and so on.
The motivating application was to define a convention for submitting orderings of the integers for the OEIS.
Gradual sequences give a natural bijection: Xn is the index of n when you sort [0..n] according to the given ordering relation.
Thus 0,1,2,... gives the normal < ordering, while 0,0,0,... is the > ordering (n Xn is the inverted ordering), and so on.
(Given gradual X and Y, what ordering is X min Y?)
This often enables interesting orderings like lexicographic, Sharkovsky etc to be encoded as a gradual sequence in a more suggestive way than just giving some initial terms in order.
Gradual sequences also appear in other contexts, so I¹d like to adopt a standard (or better) name, if there is one.
Thanks! --MLB
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