Identifier
Mp00154: Graphs —core⟶ Graphs
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
Images
=>
Cc0020;cc-rep-0Cc0020;cc-rep-1Cc0002;cc-rep-2Cc0007;cc-rep-3
([],1)=>([],1)=>[1]=>[[1]] ([],2)=>([],1)=>[1]=>[[1]] ([(0,1)],2)=>([(0,1)],2)=>[2]=>[[1,2]] ([],3)=>([],1)=>[1]=>[[1]] ([(1,2)],3)=>([(0,1)],2)=>[2]=>[[1,2]] ([(0,2),(1,2)],3)=>([(0,1)],2)=>[2]=>[[1,2]] ([(0,1),(0,2),(1,2)],3)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([],4)=>([],1)=>[1]=>[[1]] ([(2,3)],4)=>([(0,1)],2)=>[2]=>[[1,2]] ([(1,3),(2,3)],4)=>([(0,1)],2)=>[2]=>[[1,2]] ([(0,3),(1,3),(2,3)],4)=>([(0,1)],2)=>[2]=>[[1,2]] ([(0,3),(1,2)],4)=>([(0,1)],2)=>[2]=>[[1,2]] ([(0,3),(1,2),(2,3)],4)=>([(0,1)],2)=>[2]=>[[1,2]] ([(1,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,3),(1,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,2),(0,3),(1,2),(1,3)],4)=>([(0,1)],2)=>[2]=>[[1,2]] ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>[[1,2,3,4]] ([],5)=>([],1)=>[1]=>[[1]] ([(3,4)],5)=>([(0,1)],2)=>[2]=>[[1,2]] ([(2,4),(3,4)],5)=>([(0,1)],2)=>[2]=>[[1,2]] ([(1,4),(2,4),(3,4)],5)=>([(0,1)],2)=>[2]=>[[1,2]] ([(0,4),(1,4),(2,4),(3,4)],5)=>([(0,1)],2)=>[2]=>[[1,2]] ([(1,4),(2,3)],5)=>([(0,1)],2)=>[2]=>[[1,2]] ([(1,4),(2,3),(3,4)],5)=>([(0,1)],2)=>[2]=>[[1,2]] ([(0,1),(2,4),(3,4)],5)=>([(0,1)],2)=>[2]=>[[1,2]] ([(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,4),(1,4),(2,3),(3,4)],5)=>([(0,1)],2)=>[2]=>[[1,2]] ([(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(1,3),(1,4),(2,3),(2,4)],5)=>([(0,1)],2)=>[2]=>[[1,2]] ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>([(0,1)],2)=>[2]=>[[1,2]] ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>([(0,1)],2)=>[2]=>[[1,2]] ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,4),(1,3),(2,3),(2,4)],5)=>([(0,1)],2)=>[2]=>[[1,2]] ([(0,1),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>[5]=>[[1,2,3,4,5]] ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>[[1,2,3,4]] ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>[[1,2,3,4]] ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>[[1,2,3,4]] ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>[[1,2,3,4]] ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[5]=>[[1,2,3,4,5]] ([],6)=>([],1)=>[1]=>[[1]] ([(4,5)],6)=>([(0,1)],2)=>[2]=>[[1,2]] ([(3,5),(4,5)],6)=>([(0,1)],2)=>[2]=>[[1,2]] ([(2,5),(3,5),(4,5)],6)=>([(0,1)],2)=>[2]=>[[1,2]] ([(1,5),(2,5),(3,5),(4,5)],6)=>([(0,1)],2)=>[2]=>[[1,2]] ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>([(0,1)],2)=>[2]=>[[1,2]] ([(2,5),(3,4)],6)=>([(0,1)],2)=>[2]=>[[1,2]] ([(2,5),(3,4),(4,5)],6)=>([(0,1)],2)=>[2]=>[[1,2]] ([(1,2),(3,5),(4,5)],6)=>([(0,1)],2)=>[2]=>[[1,2]] ([(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(1,5),(2,5),(3,4),(4,5)],6)=>([(0,1)],2)=>[2]=>[[1,2]] ([(0,1),(2,5),(3,5),(4,5)],6)=>([(0,1)],2)=>[2]=>[[1,2]] ([(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>([(0,1)],2)=>[2]=>[[1,2]] ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2)=>[2]=>[[1,2]] ([(0,5),(1,5),(2,4),(3,4)],6)=>([(0,1)],2)=>[2]=>[[1,2]] ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,1)],2)=>[2]=>[[1,2]] ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>([(0,1)],2)=>[2]=>[[1,2]] ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>([(0,1)],2)=>[2]=>[[1,2]] ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,1)],2)=>[2]=>[[1,2]] ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2)=>[2]=>[[1,2]] ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2)=>[2]=>[[1,2]] ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2)=>[2]=>[[1,2]] ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2)=>[2]=>[[1,2]] ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,5),(1,4),(2,3)],6)=>([(0,1)],2)=>[2]=>[[1,2]] ([(1,5),(2,4),(3,4),(3,5)],6)=>([(0,1)],2)=>[2]=>[[1,2]] ([(0,1),(2,5),(3,4),(4,5)],6)=>([(0,1)],2)=>[2]=>[[1,2]] ([(1,2),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>([(0,1)],2)=>[2]=>[[1,2]] ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>[5]=>[[1,2,3,4,5]] ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,1)],2)=>[2]=>[[1,2]] ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)=>([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>[5]=>[[1,2,3,4,5]] ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>([(0,1)],2)=>[2]=>[[1,2]] ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2)=>[2]=>[[1,2]] ([(0,5),(1,5),(2,3),(2,4),(3,4)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)=>([(0,1)],2)=>[2]=>[[1,2]] ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>[[1,2,3,4]] ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>[[1,2,3,4]] ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>[[1,2,3,4]] ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>[5]=>[[1,2,3,4,5]] ([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>[[1,2,3,4]] ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>[[1,2,3,4]] ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>[[1,2,3,4]] ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>[[1,2,3,4]] ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,1)],2)=>[2]=>[[1,2]] ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)=>([(0,1)],2)=>[2]=>[[1,2]] ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)=>([(0,1)],2)=>[2]=>[[1,2]] ([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2)=>[2]=>[[1,2]] ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>[[1,2,3,4]] ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>[[1,2,3,4]] ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>[[1,2,3,4]] ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>[[1,2,3,4]] ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>[[1,2,3,4]] ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>([(0,1)],2)=>[2]=>[[1,2]] ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>[[1,2,3,4]] ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>[[1,2,3,4]] ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>[[1,2,3,4]] ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>[[1,2,3,4]] ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>[[1,2,3,4]] ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>[[1,2,3,4]] ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>[[1,2,3,4]] ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>[[1,2,3,4]] ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>[6]=>[[1,2,3,4,5,6]] ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>[[1,2,3,4]] ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>[[1,2,3,4]] ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>[[1,2,3,4]] ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>[[1,2,3,4]] ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>[[1,2,3,4]] ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>[[1,2,3,4]] ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[5]=>[[1,2,3,4,5]] ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[5]=>[[1,2,3,4,5]] ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[5]=>[[1,2,3,4,5]] ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[5]=>[[1,2,3,4,5]] ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>[[1,2,3,4]] ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>[[1,2,3,4]] ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>[[1,2,3,4]] ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>[[1,2,3]] ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>[[1,2,3,4]] ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[5]=>[[1,2,3,4,5]] ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[6]=>[[1,2,3,4,5,6]]
Map
core
Description
The core of a graph.
The core of a graph $G$ is the smallest graph $C$ such that there is a homomorphism from $G$ to $C$ and a homomorphism from $C$ to $G$.
Note that the core of a graph is not necessarily connected, see [2].
Map
to partition of connected components
Description
Return the partition of the sizes of the connected components of the graph.
Map
reading tableau
Description
Return the RSK recording tableau of the reading word of the (standard) tableau $T$ labeled down (in English convention) each column to the shape of a partition.