Identifier
There are 64 statistics on Posets in the database. There are possibly some more waiting for verification.

St000068Posets ⟶ ℤ
The number of minimal elements in a poset.
St000069Posets ⟶ ℤ
The number of maximal elements of a poset.
St000070Posets ⟶ ℤ
The number of antichains in a poset.
St000071Posets ⟶ ℤ
The number of maximal chains in a poset.
St000080Posets ⟶ ℤ
The rank of the poset.
St000100Posets ⟶ ℤ
The number of linear extensions of a poset.
St000104Posets ⟶ ℤ
The number of facets in the order polytope of this poset.
St000151Posets ⟶ ℤ
The number of facets in the chain polytope of the poset.
St000180Posets ⟶ ℤ
The number of chains of a poset.
St000181Posets ⟶ ℤ
The number of connected components of the Hasse diagram for the poset.
St000189Posets ⟶ ℤ
The number of elements in the poset.
St000281Posets ⟶ ℤ
The size of the preimage of the map 'to poset' from Binary trees to Posets.
St000282Posets ⟶ ℤ
The size of the preimage of the map 'to poset' from Ordered trees to Posets.
St000298Posets ⟶ ℤ
The order dimension or Dushnik-Miller dimension of a poset.
St000307Posets ⟶ ℤ
The number of rowmotion orbits of a poset.
St000327Posets ⟶ ℤ
The number of cover relations in a poset.
St000524Posets ⟶ ℤ
The number of posets with the same order polynomial.
St000525Posets ⟶ ℤ
The number of posets with the same zeta polynomial.
St000526Posets ⟶ ℤ
The number of posets with combinatorially isomorphic order polytopes.
St000527Posets ⟶ ℤ
The width of the poset.
St000528Posets ⟶ ℤ
The height of a poset.
St000550Posets ⟶ ℤ
The number of modular elements of a lattice.
St000551Posets ⟶ ℤ
The number of left modular elements of a lattice.
St000632Posets ⟶ ℤ
The jump number of the poset.
St000633Posets ⟶ ℤ
The size of the automorphism group of a poset.
St000634Posets ⟶ ℤ
The number of endomorphisms of a poset.
St000635Posets ⟶ ℤ
The number of strictly order preserving maps of a poset into itself.
St000639Posets ⟶ ℤ
The number of relations in a poset.
St000640Posets ⟶ ℤ
The rank of the largest boolean interval in a poset.
St000641Posets ⟶ ℤ
The number of non-empty boolean intervals in a poset.
St000642Posets ⟶ ℤ
The size of the smallest orbit of antichains under Panyushev complementation.
St000643Posets ⟶ ℤ
The size of the largest orbit of antichains under Panyushev complementation.
St000656Posets ⟶ ℤ
The number of cuts of a poset.
St000680Posets ⟶ ℤ
The Grundy value for Hackendot on posets.
St000717Posets ⟶ ℤ
The number of ordinal summands of a poset.
St000845Posets ⟶ ℤ
The maximal number of elements covered by an element in a poset.
St000846Posets ⟶ ℤ
The maximal number of elements covering an element of a poset.
St000848Posets ⟶ ℤ
The balance constant multiplied with the number of linear extensions of a poset.
St000849Posets ⟶ ℤ
The number of 1/3-balanced pairs in a poset.
St000850Posets ⟶ ℤ
The number of 1/2-balanced pairs in a poset.
St000906Posets ⟶ ℤ
The length of the shortest maximal chain in a poset.
St000907Posets ⟶ ℤ
The number of maximal antichains of minimal length in a poset.
St000908Posets ⟶ ℤ
The length of the shortest maximal antichain in a poset.
St000909Posets ⟶ ℤ
The number of maximal chains of maximal size in a poset.
St000910Posets ⟶ ℤ
The number of maximal chains of minimal length in a poset.
St000911Posets ⟶ ℤ
The number of maximal antichains of maximal size in a poset.
St000912Posets ⟶ ℤ
The number of maximal antichains in a poset.
St000914Posets ⟶ ℤ
The sum of the values of the Möbius function of a poset.
St001095Posets ⟶ ℤ
The number of non-isomorphic posets with precisely one further covering relation.
St001105Posets ⟶ ℤ
The number of greedy linear extensions of a poset.
St001106Posets ⟶ ℤ
The number of supergreedy linear extensions of a poset.
St001268Posets ⟶ ℤ
The size of the largest ordinal summand in the poset.
St001300Posets ⟶ ℤ
The rank of the boundary operator in degree 1 of the chain complex of the order complex of the poset.
St001301Posets ⟶ ℤ
The first Betti number of the order complex associated with the poset.
St001343Posets ⟶ ℤ
The dimension of the reduced incidence algebra of a poset.
St001396Posets ⟶ ℤ
Number of triples of incomparable elements in a finite poset.
St001397Posets ⟶ ℤ
Number of pairs of incomparable elements in a finite poset.
St001398Posets ⟶ ℤ
Number of subsets of size 3 of elements in a poset that form a "v".
St001399Posets ⟶ ℤ
The distinguishing number of a poset.
St001472Posets ⟶ ℤ
The permanent of the Coxeter matrix of the poset.
St001510Posets ⟶ ℤ
The number of self-evacuating linear extensions of a finite poset.
St001532Posets ⟶ ℤ
The leading coefficient of the Poincare polynomial of the poset cone.
St001533Posets ⟶ ℤ
The largest coefficient of the Poincare polynomial of the poset cone.
St001534Posets ⟶ ℤ
The alternating sum of the coefficients of the Poincare polynomial of the poset cone.