15 citations · 57 across the 35 of their papers we have counts for
36 papers
A bijection for length- patterns in permutations
Joanna N. Chen, Zhicong Lin
A bijection between -avoiding permutations and -avoiding permutations is constructed, which preserves five classical set-value…
Burstein's permutation conjecture, Hong and Li's inversion sequence conjecture, and restricted Eulerian distributions
Shane Chern, Shishuo Fu, Zhicong Lin
Recently, Hong and Li launched a systematic study of length-four pattern avoidance in inversion sequences, and in particular, they conjectured that the number of -avoiding in…
Combinatorics of Integer Partitions With Prescribed Perimeter
Zhicong Lin, Huan Xiong, Sherry H. F. Yan
We prove that the number of even parts and the number of times that parts are repeated have the same distribution over integer partitions with a fixed perimeter. This refines Strau…
Proof of Dilks' bijectivity conjecture on Baxter permutations
Zhicong Lin, Jing Liu
Baxter permutations originally arose in studying common fixed points of two commuting continuous functions. In 2015, Dilks proposed a conjectured bijection between Baxter permutati…
Combinatorics of the symmetries of ascents in restricted inversion sequences
Joanna N. Chen, Zhicong Lin
The systematic study of inversion sequences avoiding triples of relations was initiated by Martinez and Savage. For a triple , they in…
Permanent identities, combinatorial sequences, and permutation statistics
Shishuo Fu, Zhicong Lin, Zhi-Wei Sun
In this paper, we confirm six conjectures on the exact values of some permanents, relating them to the Genocchi numbers of the first and second kinds as well as the Euler numbers.…
Cycles on a multiset with only even-odd drops
Zhicong Lin, Sherry H. F. Yan
For a finite subset of , Lazar and Wachs (2019) conjectured that the number of cycles on with only even-odd drops is equal to the number of D-cycles on …
A symmetry on weakly increasing trees and multiset Schett polynomials
Zhicong Lin, Jun Ma
By considering the parity of the degrees and levels of nodes in increasing trees, a new combinatorial interpretation for the coefficients of the Taylor expansions of the Jacobi ell…
A decomposition of ballot permutations, pattern avoidance and Gessel walks
Zhicong Lin, David G. L. Wang, Tongyuan Zhao
A permutation whose any prefix has no more descents than ascents is called a ballot permutation. In this paper, we present a decomposition of ballot permutations that enables us to…
Positivity and divisibility of alternating descent polynomials
Zhicong Lin, Shi-Mei Ma, David G. L. Wang +1
The alternating descent statistic on permutations was introduced by Chebikin as a variant of the descent statistic. We show that the alternating descent polynomials on permutations…
A combinatorial bijection on di-sk trees
Shishuo Fu, Zhicong Lin, Yaling Wang
A di-sk tree is a rooted binary tree whose nodes are labeled by or , and no node has the same label as its right child. The di-sk trees are in natural bijection w…
Refined Wilf-equivalences by Comtet statistics
Shishuo Fu, Zhicong Lin, Yaling Wang
We launch a systematic study of the refined Wilf-equivalences by the statistics and , where and are the number of…
Signed Euler-Mahonian identities
Sen-Peng Eu, Zhicong Lin, Yuan-Hsun Lo
A relationship between signed Eulerian polynomials and the classical Eulerian polynomials on was given by Désarménien and Foata in 1992, and a refined version, cal…
Plateaux on generalized Stirling permutations and partial -positivity
Zhicong Lin, Jun Ma, Philip B. Zhang
We prove that the enumerative polynomials of generalized Stirling permutations by the statistics of plateaux, descents and ascents are partial -positive. Specialization of our r…
-arrangements, statistics and patterns
Shishuo Fu, Guo-Niu Han, Zhicong Lin
The -arrangements are permutations whose fixed points are -colored. We prove enumerative results related to statistics and patterns on -arrangements, confirming several co…
On -avoiding inversion and ascent sequences
Zhicong Lin, Shishuo Fu
Recently, Yan and the first named author investigated systematically the enumeration of inversion or ascent sequences avoiding vincular patterns of length , where two of the thr…
Inversion sequences avoiding pairs of patterns
Chunyan Yan, Zhicong Lin
The enumeration of inversion sequences avoiding a single pattern was initiated by Corteel--Martinez--Savage--Weselcouch and Mansour--Shattuck independently. Their work has sparked…
A new decomposition of ascent sequences and Euler--Stirling statistics
Shishuo Fu, Emma Yu Jin, Zhicong Lin +2
As shown by Bousquet-Mélou--Claesson--Dukes--Kitaev (2010), ascent sequences can be used to encode -free posets. It is known that ascent sequences are enumerated by the…
A combinatorial bijection on -noncrossing partitions
Zhicong Lin, Dongsu Kim
For any integer , we prove combinatorially the following Euler (binomial) transformation identity $$ \NC_{n+1}^{(k)}(t)=t\sum_{i=0}^n{n\choose i}\NW_{i}^{(k)}(t), $$ where…
A new encoding of permutations by Laguerre histories
Sherry H. F. Yan, Hao Zhou, Zhicong Lin
We construct a bijection from permutations to some weighted Motzkin paths known as Laguerre histories. As one application of our bijection, a neat --positivity expansion of t…
Around the -binomial-Eulerian polynomials
Zhicong Lin, David G. L. Wang, Jiang Zeng
We find a combinatorial interpretation of Shareshian and Wachs' -binomial-Eulerian polynomials, which leads to an alternative proof of their --positivity using group actio…
Restricted inversion sequences and enhanced -noncrossing partitions
Zhicong Lin
We prove a conjecture due independently to Yan and Martinez--Savage that asserts inversion sequences with no weakly decreasing subsequence of length and enhanced -noncrossin…
Refined restricted inversion sequences
Dongsu Kim, Zhicong Lin
Recently, the study of patterns in inversion sequences was initiated by Corteel-Martinez-Savage-Weselcouch and Mansour-Shattuck independently. Motivated by their works and a double…
A sextuple equidistribution arising in Pattern Avoidance
Zhicong Lin, Dongsu Kim
We construct an intriguing bijection between -avoiding inversion sequences and -avoiding permutations, which proves a sextuple equidistribution involving double E…