@article{chen2025DM,
title = {Bijections around Springer numbers},
journal = {Discrete Mathematics},
volume = {348},
number = {11},
pages = {114570},
year = {2025},
issn = {0012-365X},
doi = {https://doi.org/10.1016/j.disc.2025.114570},
url = {https://www.sciencedirect.com/science/article/pii/S0012365X25001785},
author = {Shaoshi Chen and Yang Li and Zhicong Lin and Sherry H.F. Yan},
keywords = {Springer numbers, Snakes, Alternating permutations, Labeled ballot paths},
abstract = {Arnol'd proved in 1992 that Springer numbers enumerate the snakes, which are type B analogs of alternating permutations. Chen, Fan and Jia in 2011 introduced the labeled ballot paths and established a “hard” bijection with snakes. Callan conjectured in 2012 and Han–Kitaev–Zhang proved recently that rc-invariant alternating permutations are counted by Springer numbers. Very recently, Chen–Fang–Kitaev–Zhang investigated multi-dimensional permutations and proved that weakly increasing 3-dimensional permutations are also counted by Springer numbers. In this work, we construct a sequence of “natural” bijections linking the above four combinatorial objects.}
}