Identifier
Values
=>
Cc0028;cc-rep-0 Cc0014;cc-rep-1 Cc0029;cc-rep-2 Cc0014;cc-rep
[[1],[]]=>([],1)=>([(0,1)],2)=>([(0,1)],2)=>1 [[2],[]]=>([(0,1)],2)=>([(0,2),(2,1)],3)=>([(0,2),(2,1)],3)=>1 [[1,1],[]]=>([(0,1)],2)=>([(0,2),(2,1)],3)=>([(0,2),(2,1)],3)=>1 [[2,1],[1]]=>([],2)=>([(0,1),(0,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2 [[3],[]]=>([(0,2),(2,1)],3)=>([(0,3),(2,1),(3,2)],4)=>([(0,3),(2,1),(3,2)],4)=>1 [[2,1],[]]=>([(0,1),(0,2)],3)=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>2 [[3,1],[1]]=>([(1,2)],3)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>3 [[2,2],[1]]=>([(0,2),(1,2)],3)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2 [[3,2],[2]]=>([(1,2)],3)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>3 [[1,1,1],[]]=>([(0,2),(2,1)],3)=>([(0,3),(2,1),(3,2)],4)=>([(0,3),(2,1),(3,2)],4)=>1 [[2,2,1],[1,1]]=>([(1,2)],3)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>3 [[2,1,1],[1]]=>([(1,2)],3)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>3 [[4],[]]=>([(0,3),(2,1),(3,2)],4)=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1 [[2,2],[]]=>([(0,1),(0,2),(1,3),(2,3)],4)=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>2 [[1,1,1,1],[]]=>([(0,3),(2,1),(3,2)],4)=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1 [[5],[]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>1 [[1,1,1,1,1],[]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>1
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Description
The number of greedy linear extensions of a poset.
A linear extension of a poset $P$ with elements $\{x_1,\dots,x_n\}$ is greedy, if it can be obtained by the following algorithm:
  • Step 1. Choose a minimal element $x_1$.
  • Step 2. Suppose $X=\{x_1,\dots,x_i\}$ have been chosen. If there is at least one minimal element of $P\setminus X$ which is greater than $x_i$ then choose $x_{i+1}$ to be any such minimal element; otherwise, choose $x_{i+1}$ to be any minimal element of $P\setminus X$.
This statistic records the number of greedy linear extensions.
Map
to poset
Description
Return the poset corresponding to the lattice.
Map
order ideals
Description
The lattice of order ideals of a poset.
An order ideal $\mathcal I$ in a poset $P$ is a downward closed set, i.e., $a \in \mathcal I$ and $b \leq a$ implies $b \in \mathcal I$. This map sends a poset to the lattice of all order ideals sorted by inclusion with meet being intersection and join being union.
Map
cell poset
Description
The Young diagram of a skew partition regarded as a poset.
This is the poset on the cells of the Young diagram, such that a cell $d$ is greater than a cell $c$ if the entry in $d$ must be larger than the entry of $c$ in any standard Young tableau on the skew partition.