Hi, Well I think that "dinv" would be "number_of_diagonal_inversions" but I agree with Hugh, the statistics area(D), bounce(D) and dinv(D) are all fairly standard (add Haglund's book + dozens of references since) and certainly way more descriptive than "a_statistic", "b_statistic" and "d_statistic"; however the advantage of those descriptors is that they indicate their equi-distribution over the set of Dyck paths (that is, \sum_D q^{x(D)} is the q-Catalan for x = a,b,d-statistic).
Just a word about bounce(D) though: it is sort of a major index of the touch points of the bounce path. There are the obvious involutions on the touch point set (complementation and reverse) and I think I have seen the size_of_the_set_of_touch_points_of_the_bounce_path(D) come up in a formula somewhere. -Mike On Thursday, 17 May 2012 12:40:43 UTC-4, Hugh Thomas wrote: > > > Hi! > > I think "area", "bounce", and "dinv" are standard terms. Spelling out > what "dinv" means would only confuse matters for me. I don't remember the > precise definition --- it is complicated. So even spelling outtwo or three > words would still be only be able to give an imprecise description. That > being the case, I think the best thing is to use the standard term. > > cheers, > > Hugh > > On Thursday, May 17, 2012 5:45:19 AM UTC-3, Christian Stump wrote: >> >> Hi, >> >> I am currently working on filling the wiki at www.findstat.org with >> more data, since Chris Berg and I are going to present it at the FPSAC >> this summer. >> >> I would like to make the following changes to Dyck words: >> >> 1. changing a-statistic, b-statistic, d-statistic to area, bounce, >> dinv (and leaving the old with a warning). >> 2. changing the to_partition to return the partition when cutting out >> the path above the diagonal (currently, the transposed is returned). >> >> Is that okay with everyone? >> >> Christian >> > -- You received this message because you are subscribed to the Google Groups "sage-combinat-devel" group. To view this discussion on the web visit https://groups.google.com/d/msg/sage-combinat-devel/-/OOftO57Yu2cJ. To post to this group, send email to sage-combinat-devel@googlegroups.com. To unsubscribe from this group, send email to sage-combinat-devel+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sage-combinat-devel?hl=en.