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Symmetries on vector parking functions via bounded lattice paths
Wenjie Fang, Yang Li, Zhicong Lin
Partly motivated by enumeration of parking functions and their variants, there is a long-standing interest in lattice paths refined by several statistics, including the notable $\m…
Bijective proofs of several conjectures on Jacobi permutations
Zhicong Lin, Yongzhou Wen, Sherry H. F. Yan
Jacobi permutations, invented by Viennot in the context of the Jacobi elliptic functions, are counted by the Euler numbers. Recently, Henke, Hoffman, Stephens, Yuan, and Zhuang stu…
A bijection between - and -avoiding permutations preserving -stack-sortability
Yang Li, Sergey Kitaev, Zhicong Lin +1
We construct a bijection between - and -avoiding permutations that preserves the property of -stack-sortability. Our bijection transforms natural statistics between th…
Bijections in weakly increasing trees via binary trees
Yang Li, Zhicong Lin
As a unification of increasing trees and plane trees, the weakly increasing trees labeled by a multiset was introduced by Lin-Ma-Ma-Zhou in 2021. Motived by some symmetries in plan…
Combinatorics on bi--positivity of -Eulerian polynomials
Sherry H. F. Yan, Xubo Yang, Zhicong Lin
The -Eulerian polynomials were introduced as ascent polynomials over -inversion sequences by Savage and Viswanathan. The bi--positivity of the -Eul…
Bijections around Springer numbers
Shaoshi Chen, Yang Li, Zhicong Lin +1
Arnol'd proved in 1992 that Springer numbers enumerate the Snakes, which are type analogs of alternating permutations. Chen, Fan and Jia in 2011 introduced the labeled ballot p…
Parity statistics on restricted permutations and the Catalan--Schett polynomials
Zhicong Lin, Jing Liu, Sherry H. F. Yan
Motivated by Kitaev and Zhang's recent work on non-overlapping ascents in stack-sortable permutations and Dumont's permutation interpretation of the Jacobi elliptic functions, we i…
On a conjecture concerning the -Euler-Mahonian statistic on permutations
Kaimei Huang, Zhicong Lin, Sherry H. F. Yan
A pair of permutation statistics is said to be -Euler-Mahonian if and , are e…
Two involutions on binary trees and generalizations
Yang Li, Zhicong Lin, Tongyuan Zhao
This paper investigates two involutions on binary trees. One is the mirror symmetry of binary trees which combined with the classical bijection between binary trees and plane t…