Random observations from the FindStat project discussed at the wordpress blog blog.findstat.org.
We believe that the FindStat database contains many interesting connections – most of which are probably known, but others are yet to be found and proven. We created this blog to post statistics that appear to be connected through combinatorial maps between various combinatorial collections, and
- which we think are worth sharing, and
- for which we would like to ask the community to come up with an explanation.
We only post connections that we find surprising, seeking for a (more or less) detailed explanation or a reference in the literature. If it turns out that we find multiple interesting and unexpected connections (previously known and unknown), we plan to publish these connections. Before doing so, we will ask anyone who contributed a solution or reference, for his/her agreement for including it with a corresponding acknowledgement in the publication. Obviously, this will only happen once we have collected enough connections, most likely not within the first year of this blog.
FindStatFact 3 is a simple observation of two coinciding statistics on integer partitions in a paper from 2007 that FindStat's search discovered.
FindStatFact 2 is about describing the weak exceedances on permutations in terms of Dyck paths
FindStatFact 1 is about the connection of two classes of statistics on Dyck paths, namely Narayana statistics and the area statistic