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math.CO2025
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…
math.CO2025
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…
math.CO2025
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…