# FindStat - the combinatorial statistics database

@article{Berg2014FindStatT, title={FindStat - the combinatorial statistics database}, author={Chris Berg and Viviane Pons and Travis Scrimshaw and Jessica Striker and Christian Stump}, journal={ArXiv}, year={2014}, volume={abs/1401.3690} }

The FindStat project at www.FindStat.org provides an online platform for mathematicians, particularly for combinatorialists, to gather information about combinatorial statistics and their relations. This outline provides an overview over the project.

## 18 Citations

Homomesies on permutations -- an analysis of maps and statistics in the FindStat database

- Mathematics
- 2022

In this paper, we perform a systematic study of permutation statistics and bijective maps on permutations in which we identify and prove 122 instances of the homomesy phenomenon. Homomesy occurs when…

ZEN AND THE ART OF DATABASE MAINTENANCE

- Computer Science
- 2020

This work reports on the transition of the L-functions and Modular Forms Database between two database systems, and highlights some of the improvements that are made as part of this transition.

DiscreteZOO: Towards a Fingerprint Database of Discrete Objects

- Computer ScienceICMS
- 2018

The DiscreteZOO project is presented, a repository and a fingerprint database for discrete mathematical objects that aims to become a general platform to make collections of mathematical objects easier to publish and access.

Euler-Catalan's Number Triangle and Its Application

- MathematicsSymmetry
- 2020

On the basis of properties of Catalan's and Euler's triangles, an explicit formula is obtained that counts the total number of such combinatorial objects and a bivariate generating function.

The set of alternating sign matrices which are determined by their X-ray is a member of the Catalan family

- Mathematics
- 2017

We exhibit a bijection between Dyck paths and alternating sign matrices which are determined by their antidiagonal sums.

The rank enumeration of certain parabolic non-crossing partitions

- MathematicsAlgebraic Combinatorics
- 2022

We consider $m$-divisible non-crossing partitions of $\{1,2,\ldots,mn\}$ with the property that for some $t\leq n$ no block contains more than one of the first $t$ integers. We give a closed formula…

Expected value of letters of permutations with a given number of $k$-cycles

- Mathematics
- 2021

6 Acknowledgments 21 In this paper, we study permutations π ∈ Sn with exactly m transpositions. In particular, we are interested in the expected value of π(1) when such permutations are chosen…

Gamma expansions of $q$-Narayana polynomials, pattern avoidance and the $(-1)$-phenomenon

- Mathematics
- 2018

The aim of this paper is two-folded. We first prove several new interpretations of a kind of $q$-Narayana polynomials along with their corresponding $\gamma$-expansions using pattern avoiding…

Probabilistic Limit Theorems for the Coefficients of a Class of Root-Unitary Polynomials

- Mathematics
- 2022

Sequences of discrete random variables are studied whose probability generating functions have roots located on the unit circle in the complex plane. Bounds on the cumulants of all orders for a class…

The Newton polytope and Lorentzian property of chromatic symmetric functions

- Mathematics
- 2022

A BSTRACT . Chromatic symmetric functions are well-studied symmetric functions in algebraic combinatorics that generalize the chromatic polynomial and are related to Hessenberg varieties and diagonal…

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