

A139561


Growth function for the relatively free monoid on three generators with identity xyzyx = yxzxy.


0




OFFSET

0,2


COMMENTS

A semigroup which satisfies the identity xyzyx=yxzxy is called nilpotent of class 2 in the Malcev sense. Initially this sequence looks very like A140348, which counts the words that are distinct in the free nil2 group.
The sequences first differ at n=7, where there are six equations that hold for the group but do not follow from the Malcev identity, e.g. abccaab = caabbca. Cancellation is not assumed and does not hold, so despite the fact that the former equation does not follow from the Malcev identity, aabccaab = acaabbca does follow.
Shneerson has shown that this sequence grows roughly like some power of n^logn . Contrast to A140348, which has polynomial growth.


REFERENCES

L. M. Shneerson, Relatively free semigroups of intermediate growth, J. Algebra, 235 (2001) 484546.


LINKS

Table of n, a(n) for n=0..8.


EXAMPLE

Substituting x>a, y>b, z>1 in the identity gives abba=baab, this is the smallest example.
Substituting x>ab, y>b, z>c in the identity gives abbcbab=babcabb.


CROSSREFS

Cf. A140348.
Sequence in context: A269488 A027027 A140348 * A152169 A241574 A268013
Adjacent sequences: A139558 A139559 A139560 * A139562 A139563 A139564


KEYWORD

nonn


AUTHOR

David S. Newman and Moshe Shmuel Newman, Jun 10 2008


STATUS

approved



