Identifier
Values
[[1]] => [(1,2)] => [2,1] => 0
[[1,0],[0,1]] => [(1,4),(2,3)] => [3,4,2,1] => 0
[[0,1],[1,0]] => [(1,2),(3,4)] => [2,1,4,3] => 0
[[1,0,0],[0,1,0],[0,0,1]] => [(1,6),(2,5),(3,4)] => [4,5,6,3,2,1] => 0
[[0,1,0],[1,0,0],[0,0,1]] => [(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => 0
[[1,0,0],[0,0,1],[0,1,0]] => [(1,6),(2,3),(4,5)] => [3,5,2,6,4,1] => 0
[[0,1,0],[1,-1,1],[0,1,0]] => [(1,2),(3,6),(4,5)] => [2,1,5,6,4,3] => 1
[[0,0,1],[1,0,0],[0,1,0]] => [(1,6),(2,3),(4,5)] => [3,5,2,6,4,1] => 0
[[0,1,0],[0,0,1],[1,0,0]] => [(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => 0
[[0,0,1],[0,1,0],[1,0,0]] => [(1,4),(2,3),(5,6)] => [3,4,2,1,6,5] => 0
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searching the database for the individual values of this statistic
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searching the database for statistics with the same generating function
Description
The number of occurrences of 14-2-3 or 14-3-2.
The number of permutations avoiding both of these patterns is the case $k=2$ of the third item in Corollary 34 of [1].
Map
non-nesting-exceedence permutation
Description
The fixed-point-free permutation with deficiencies given by the perfect matching, no alignments and no inversions between exceedences.
Put differently, the exceedences form the unique non-nesting perfect matching whose openers coincide with those of the given perfect matching.
Map
link pattern
Description
Sends an alternating sign matrix to the link pattern of the corresponding fully packed loop configuration.