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math.CO2022
On the lattice of weighted partitions
Keiichi Shigechi
We introduce and study the lattice of generalized partitions, called weighted partitions. This lattice possesses similar properties of the lattice of partitions. By use of the pict…
math.CO2022
From dimer models to generalized lattice paths
Keiichi Shigechi
A recurrence relation of the generating function of the dimer model of Fibonacci type gives a functional relation for formal power series associated to lattice paths such as a Dyck…
math.CO2022
Noncommutative crossing partitions
Keiichi Shigechi
We define and study noncommutative crossing partitions which are a generalization of non-crossing partitions. By introducing a new cover relation on binary trees, we show that the…