The forgotten monoid

Details The forgotten monoid The forgotten monoid

2007-06-20

arxiv.org/abs/0706.2996v3

RIMS Kokyuroku Bessatsu B8 (2008) 71-83

Mathematics

Combinatorics

13 pages; in version 3 the proof of Proposition 3 is corrected

Scientific paper

We study properties of the forgotten monoid which appeared in work of Lascoux and Schutzenberger and recently resurfaced in the construction of dual equivalence graphs by Assaf. In particular, we provide an explicit characterization of the forgotten classes in terms of inversion numbers and show that there are n^2-3n+4 forgotten classes in the symmetric group S_n. Each forgotten class contains a canonical element that can be characterized by pattern avoidance. We also show that the sum of Gessel's quasi-symmetric functions over a forgotten class is a 0-1 sum of ribbon-Schur functions.

Affiliated with

Also associated with

No associations

Rating

The forgotten monoid does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The forgotten monoid, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The forgotten monoid will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-34436