There are

(and possibly some waiting for verification)

**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.