There are 47 statistics on Perfect matchings in the database:
(and possibly some waiting for verification)

St000041Perfect matchings ⟶ ℤ
The number of nestings of a perfect matching.
St000042Perfect matchings ⟶ ℤ
The number of crossings of a perfect matching.
St000043Perfect matchings ⟶ ℤ
The number of crossings plus two-nestings of a perfect matching.
St000044Perfect matchings ⟶ ℤ
The number of vertices of the unicellular map given by a perfect matching.
St000164Perfect matchings ⟶ ℤ
The number of short pairs.
St000719Perfect matchings ⟶ ℤ
The number of alignments in a perfect matching.
St000720Perfect matchings ⟶ ℤ
The size of the largest partition in the oscillating tableau corresponding to the perfect matching.
St000721Perfect matchings ⟶ ℤ
The sum of the partition sizes in the oscillating tableau corresponding to a perfect matching.
St000746Perfect matchings ⟶ ℤ
The number of pairs with odd minimum in a perfect matching.
St000754Perfect matchings ⟶ ℤ
The Grundy value for the game of removing nestings in a perfect matching.
St000780Perfect matchings ⟶ ℤ
The size of the orbit under rotation of a perfect matching.
St000782Perfect matchings ⟶ ℤ
The indicator function of whether a given perfect matching is an L & P matching.
St000787Perfect matchings ⟶ ℤ
The number of flips required to make a perfect matching noncrossing.
St000788Perfect matchings ⟶ ℤ
The number of nesting-similar perfect matchings of a perfect matching.
St000789Perfect matchings ⟶ ℤ
The number of crossing-similar perfect matchings of a perfect matching.
St000819Perfect matchings ⟶ ℤ
The propagating number of a perfect matching.
St000838Perfect matchings ⟶ ℤ
The number of terminal right-hand endpoints when the vertices are written in order.
St000840Perfect matchings ⟶ ℤ
The number of closers smaller than the largest opener in a perfect matching.
St000841Perfect matchings ⟶ ℤ
The largest opener of a perfect matching.
St000843Perfect matchings ⟶ ℤ
The decomposition number of a perfect matching.
St000924Perfect matchings ⟶ ℤ
The number of topologically connected components of a perfect matching.
St000945Perfect matchings ⟶ ℤ
The number of matchings in the dihedral orbit of a perfect matching.
St001040Perfect matchings ⟶ ℤ
The depth of the decreasing labelled binary unordered tree associated with the perfect matching.
St001041Perfect matchings ⟶ ℤ
The depth of the label 1 in the decreasing labelled binary unordered tree associated with the perfect matching.
St001042Perfect matchings ⟶ ℤ
The size of the automorphism group of the leaf labelled binary unordered tree associated with the perfect matching.
St001043Perfect matchings ⟶ ℤ
The depth of the leaf closest to the root in the binary unordered tree associated with the perfect matching.
St001044Perfect matchings ⟶ ℤ
The number of pairs whose larger element is at most one more than half the size of the perfect matching.
St001045Perfect matchings ⟶ ℤ
The number of leaves in the subtree not containing one in the decreasing labelled binary unordered tree associated with the perfect matching.
St001046Perfect matchings ⟶ ℤ
The maximal number of arcs nesting a given arc of a perfect matching.
St001047Perfect matchings ⟶ ℤ
The maximal number of arcs crossing a given arc of a perfect matching.
St001048Perfect matchings ⟶ ℤ
The number of leaves in the subtree containing 1 in the decreasing labelled binary unordered tree associated with the perfect matching.
St001049Perfect matchings ⟶ ℤ
The smallest label in the subtree not containing 1 in the decreasing labelled binary unordered tree associated with the perfect matching.
St001131Perfect matchings ⟶ ℤ
The number of trivial trees on the path to label one in the decreasing labelled binary unordered tree associated with the perfect matching.
St001132Perfect matchings ⟶ ℤ
The number of leaves in the subtree whose sister has label 1 in the decreasing labelled binary unordered tree associated with the perfect matching.
St001133Perfect matchings ⟶ ℤ
The smallest label in the subtree rooted at the sister of 1 in the decreasing labelled binary unordered tree associated with the perfect matching.
St001134Perfect matchings ⟶ ℤ
The largest label in the subtree rooted at the sister of 1 in the leaf labelled binary unordered tree associated with the perfect matching.
St001136Perfect matchings ⟶ ℤ
The largest label with larger sister in the leaf labelled binary unordered tree associated with the perfect matching.
St001152Perfect matchings ⟶ ℤ
The number of pairs with even minimum in a perfect matching.
St001444Perfect matchings ⟶ ℤ
The rank of the skew-symmetric form which is non-zero on crossing arcs of a perfect matching.
St001589Perfect matchings ⟶ ℤ
The nesting number of a perfect matching.
St001590Perfect matchings ⟶ ℤ
The crossing number of a perfect matching.
St001830Perfect matchings ⟶ ℤ
The chord expansion number of a perfect matching.
St001831Perfect matchings ⟶ ℤ
The multiplicity of the non-nesting perfect matching in the chord expansion of a perfect matching.
St001832Perfect matchings ⟶ ℤ
The number of non-crossing perfect matchings in the chord expansion of a perfect matching.
St001835Perfect matchings ⟶ ℤ
The number of occurrences of a 231 pattern in the restricted growth word of a perfect matching.
St001836Perfect matchings ⟶ ℤ
The number of occurrences of a 213 pattern in the restricted growth word of a perfect matching.
St001837Perfect matchings ⟶ ℤ
The number of occurrences of a 312 pattern in the restricted growth word of a perfect matching.