6 papers
When arrow patterns meet classical patterns
Shishuo Fu, Zhenghe Yang
Seeking to bridge the structural divide between a permutation's cycle notation and its one-line notation, Berman and Tenner introduced a novel notion of permutation pattern known a…
Parity patterns meet Genocchi numbers, I: four labelings and three bijections
Quan Yuan, Qi Fang, Shishuo Fu +1
Hetyei introduced in 2019 the homogenized Linial arrangement and showed that its regions are counted by the median Genocchi numbers. In the course of devising a different proof of…
On fourteen equidistribution conjectures of Lv and Zhang and monotone mesh patterns with corner shadings
Qi Fang, Shishuo Fu, Sergey Kitaev +1
Three complementation-like involutions are constructed on permutations to prove, and in some cases generalize, all remaining fourteen joint symmetric equidistribution conjectures o…
Consecutive and quasi-consecutive patterns: -Wilf classifications and generating functions
Yan Wang, Qi Fang, Shishuo Fu +2
Motivated by a correlation between the distribution of descents over permutations that avoid a consecutive pattern and those avoiding the respective quasi-consecutive pattern, as e…
Sequences of odd length in strict partitions II: the -measure and refinements of Euler's theorem
Shishuo Fu, Haijun Li
The number of sequences of odd length in strict partitions (denoted as ), which plays a pivotal role in the first paper of this series, is investigated in different c…
Sequences of odd length in strict partitions I: the combinatorics of double sum Rogers-Ramanujan type identities
Shishuo Fu, Haijun Li
Strict partitions are enumerated with respect to the weight, the number of parts, and the number of sequences of odd length. We write this trivariate generating function as a doubl…