- FindStat

— database and search engine for combinatorial statistics and maps —

This collaborative project is

a database of combinatorial statistics and maps on combinatorial collections and
a search engine, identifying your data as the composition of known maps and statistics.

a combinatorial collection is a collection $\mathcal{S} = \bigcup_{x}\mathcal{S}_x$ of finite sets $\mathcal{S}_x$ (e.g. the set of permutations)
a combinatorial map is a map $\phi: \mathcal{S} \longrightarrow \mathcal{S'}$ between collections (e.g. the inverse of a permutation)
a combinatorial statistic (or parameter) is a map $\operatorname{st}: \mathcal{S} \longrightarrow \mathbb{Z}$ (e.g. the order of a permutation)
the database currently contains 1964 statistics and 329 maps on 24 collections

There is a detailed usage example and several MathOverflow discussions with examples of the database usage.

You may also consult a discussion of the FindStat project that we compiled for FPSAC 2019 conference.

Examples of mathematical research questions that can be answered using this project:

My research produces an integer for each graph. What are these integers? (ex1 / ex2)
I have a bijection on Dyck paths. Can it be obtained from known bijections?
I have a function $f(x,y) \in \mathbb{N}[x,y]$ with $f(1,1) = n!$ . What do the coefficients count? (ex1)
I have a decomposition of integer partitions into disjoint sets. Is there a combinatorial rule explaining it?
I have two combinatorial rules to compute integers for each permutation. How are they related? (ex1 / ex2)
I have two sets of binary trees of the same size. Is there a bijection between the two?

go to statistic finder

go to map finder

search for keyword

contact the FindStat team at info@findstat.org