- FindStat

edit this map or download as text // json

Identifier

Mp00306: Posets —rowmotion cycle type⟶ Integer partitions

Images

([],1) => [2]

([],2) => [2,2]

([(0,1)],2) => [3]

([],3) => [2,2,2,2]

([(1,2)],3) => [6]

([(0,1),(0,2)],3) => [3,2]

([(0,2),(2,1)],3) => [4]

([(0,2),(1,2)],3) => [3,2]

([],4) => [2,2,2,2,2,2,2,2]

([(2,3)],4) => [6,6]

([(1,2),(1,3)],4) => [6,2,2]

([(0,1),(0,2),(0,3)],4) => [3,2,2,2]

([(0,2),(0,3),(3,1)],4) => [7]

([(0,1),(0,2),(1,3),(2,3)],4) => [4,2]

([(1,2),(2,3)],4) => [4,4]

([(0,3),(3,1),(3,2)],4) => [4,2]

([(1,3),(2,3)],4) => [6,2,2]

([(0,3),(1,3),(3,2)],4) => [4,2]

([(0,3),(1,3),(2,3)],4) => [3,2,2,2]

([(0,3),(1,2)],4) => [3,3,3]

([(0,3),(1,2),(1,3)],4) => [5,3]

([(0,2),(0,3),(1,2),(1,3)],4) => [3,2,2]

([(0,3),(2,1),(3,2)],4) => [5]

([(0,3),(1,2),(2,3)],4) => [7]

([],5) => [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]

([(3,4)],5) => [6,6,6,6]

([(2,3),(2,4)],5) => [6,6,2,2,2,2]

([(1,2),(1,3),(1,4)],5) => [6,2,2,2,2,2,2]

([(0,1),(0,2),(0,3),(0,4)],5) => [3,2,2,2,2,2,2,2]

([(0,2),(0,3),(0,4),(4,1)],5) => [7,6]

([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => [7,2,2]

([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => [4,2,2,2]

([(1,3),(1,4),(4,2)],5) => [14]

([(0,3),(0,4),(4,1),(4,2)],5) => [7,2,2]

([(1,2),(1,3),(2,4),(3,4)],5) => [4,4,2,2]

([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => [5,2]

([(0,3),(0,4),(3,2),(4,1)],5) => [4,3,3]

([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => [5,4]

([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => [4,2,2]

([(2,3),(3,4)],5) => [4,4,4,4]

([(1,4),(4,2),(4,3)],5) => [4,4,2,2]

([(0,4),(4,1),(4,2),(4,3)],5) => [4,2,2,2]

([(2,4),(3,4)],5) => [6,6,2,2,2,2]

([(1,4),(2,4),(4,3)],5) => [4,4,2,2]

([(0,4),(1,4),(4,2),(4,3)],5) => [4,2,2]

([(1,4),(2,4),(3,4)],5) => [6,2,2,2,2,2,2]

([(0,4),(1,4),(2,4),(4,3)],5) => [4,2,2,2]

([(0,4),(1,4),(2,4),(3,4)],5) => [3,2,2,2,2,2,2,2]

([(0,4),(1,4),(2,3)],5) => [6,3,3,3]

([(0,4),(1,3),(2,3),(2,4)],5) => [8,3,2]

([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => [5,3,2,2]

([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => [3,2,2,2,2]

([(0,4),(1,4),(2,3),(4,2)],5) => [5,2]

([(0,4),(1,3),(2,3),(3,4)],5) => [7,2,2]

([(0,4),(1,4),(2,3),(2,4)],5) => [6,5,3]

([(0,4),(1,4),(2,3),(3,4)],5) => [7,6]

([(1,4),(2,3)],5) => [6,6,6]

([(1,4),(2,3),(2,4)],5) => [10,6]

([(0,4),(1,2),(1,4),(2,3)],5) => [8,3]

([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => [5,4]

([(1,3),(1,4),(2,3),(2,4)],5) => [6,2,2,2,2]

([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => [7,2]

([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => [4,2,2]

([(0,4),(1,2),(1,4),(4,3)],5) => [10]

([(0,4),(1,2),(1,3)],5) => [6,3,3,3]

([(0,4),(1,2),(1,3),(1,4)],5) => [6,5,3]

([(0,2),(0,4),(3,1),(4,3)],5) => [5,4]

([(0,4),(1,2),(1,3),(3,4)],5) => [10,2]

([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => [8]

([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => [7,2,2]

([(0,3),(0,4),(1,2),(1,4)],5) => [8,3,2]

([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => [5,3,2,2]

([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => [3,2,2,2,2]

([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => [10]

([(0,3),(1,2),(1,4),(3,4)],5) => [8,3]

([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => [7,2]

([(1,4),(3,2),(4,3)],5) => [10]

([(0,3),(3,4),(4,1),(4,2)],5) => [5,2]

([(1,4),(2,3),(3,4)],5) => [14]

([(0,4),(1,2),(2,4),(4,3)],5) => [8]

([(0,3),(1,4),(4,2)],5) => [12]

([(0,4),(3,2),(4,1),(4,3)],5) => [8]

([(0,4),(1,2),(2,3),(2,4)],5) => [10]

([(0,4),(2,3),(3,1),(4,2)],5) => [6]

([(0,3),(1,2),(2,4),(3,4)],5) => [4,3,3]

([(0,4),(1,2),(2,3),(3,4)],5) => [5,4]

([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [5,2]

([],6) => [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]

([(4,5)],6) => [6,6,6,6,6,6,6,6]

([(3,4),(3,5)],6) => [6,6,6,6,2,2,2,2,2,2,2,2]

([(2,3),(2,4),(2,5)],6) => [6,6,2,2,2,2,2,2,2,2,2,2,2,2]

([(1,2),(1,3),(1,4),(1,5)],6) => [6,2,2,2,2,2,2,2,2,2,2,2,2,2,2]

([(0,1),(0,2),(0,3),(0,4),(0,5)],6) => [3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]

([(0,2),(0,3),(0,4),(0,5),(5,1)],6) => [7,6,6,6]

([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6) => [7,6,2,2,2,2]

([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6) => [7,2,2,2,2,2,2]

([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6) => [4,2,2,2,2,2,2,2]

([(1,3),(1,4),(1,5),(5,2)],6) => [14,6,6]

([(0,3),(0,4),(0,5),(5,1),(5,2)],6) => [7,6,2,2,2,2]

([(1,2),(1,3),(1,4),(3,5),(4,5)],6) => [14,2,2,2,2]

([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => [4,4,2,2,2,2,2,2]

>>> Load all 2517 entries. <<<

click to show experimental identities (only identities of compositions of up to three maps are shown)

Description

The cycle type of rowmotion on the order ideals of a poset.

Sage code

def mapping(P):
    P = P.canonical_label()
    J = P.antichains(lambda a: frozenset(P.order_ideal(a)))
    if J.cardinality() > 500:
        raise ValueError("Poset has too many order ideals for this map")
    D = DiscreteDynamicalSystem(J, lambda I: P.rowmotion(I), inverse=True, is_finite=True)
    return Partition(sorted([len(o) for o in D.cycles()], reverse=True))

Weight

Created

Jul 13, 2023 at 15:54 by Martin Rubey

Updated

Jul 13, 2023 at 15:54 by Martin Rubey