- FindStat

edit this statistic or download as text // json

Identifier

St000170: Semistandard tableaux ⟶ ℤ

Values

[[1]] => 1

[[2]] => 2

[[3]] => 3

[[4]] => 4

[[5]] => 5

[[6]] => 6

[[1,1]] => 1

[[1,2]] => 1

[[2,2]] => 2

[[1],[2]] => 1

[[1,3]] => 1

[[2,3]] => 2

[[3,3]] => 3

[[1],[3]] => 1

[[2],[3]] => 2

[[1,4]] => 1

[[2,4]] => 2

[[3,4]] => 3

[[4,4]] => 4

[[1],[4]] => 1

[[2],[4]] => 2

[[3],[4]] => 3

[[1,5]] => 1

[[2,5]] => 2

[[3,5]] => 3

[[4,5]] => 4

[[5,5]] => 5

[[1],[5]] => 1

[[2],[5]] => 2

[[3],[5]] => 3

[[4],[5]] => 4

[[1,6]] => 1

[[2,6]] => 2

[[3,6]] => 3

[[4,6]] => 4

[[5,6]] => 5

[[6,6]] => 6

[[1],[6]] => 1

[[2],[6]] => 2

[[3],[6]] => 3

[[4],[6]] => 4

[[5],[6]] => 5

[[1,1,1]] => 1

[[1,1,2]] => 1

[[1,2,2]] => 1

[[2,2,2]] => 2

[[1,1],[2]] => 1

[[1,2],[2]] => 1

[[1,1,3]] => 1

[[1,2,3]] => 1

[[1,3,3]] => 1

[[2,2,3]] => 2

[[2,3,3]] => 2

[[3,3,3]] => 3

[[1,1],[3]] => 1

[[1,2],[3]] => 1

[[1,3],[2]] => 1

[[1,3],[3]] => 1

[[2,2],[3]] => 2

[[2,3],[3]] => 2

[[1],[2],[3]] => 1

[[1,1,4]] => 1

[[1,2,4]] => 1

[[1,3,4]] => 1

[[1,4,4]] => 1

[[2,2,4]] => 2

[[2,3,4]] => 2

[[2,4,4]] => 2

[[3,3,4]] => 3

[[3,4,4]] => 3

[[4,4,4]] => 4

[[1,1],[4]] => 1

[[1,2],[4]] => 1

[[1,4],[2]] => 1

[[1,3],[4]] => 1

[[1,4],[3]] => 1

[[1,4],[4]] => 1

[[2,2],[4]] => 2

[[2,3],[4]] => 2

[[2,4],[3]] => 2

[[2,4],[4]] => 2

[[3,3],[4]] => 3

[[3,4],[4]] => 3

[[1],[2],[4]] => 1

[[1],[3],[4]] => 1

[[2],[3],[4]] => 2

[[1,1,5]] => 1

[[1,2,5]] => 1

[[1,3,5]] => 1

[[1,4,5]] => 1

[[1,5,5]] => 1

[[2,2,5]] => 2

[[2,3,5]] => 2

[[2,4,5]] => 2

[[2,5,5]] => 2

[[3,3,5]] => 3

[[3,4,5]] => 3

[[3,5,5]] => 3

[[4,4,5]] => 4

[[4,5,5]] => 4

[[5,5,5]] => 5

>>> Load all 923 entries. <<<

search for individual values

searching the database for the individual values of this statistic

/ search for generating function

searching the database for statistics with the same generating function

click to show known generating functions

Description

The trace of a semistandard tableau.
This is the sum of the entries on the diagonal.

References

[1] Stanley, R. P. The conjugate trace and trace of a plane partition MathSciNet:0309748
[2] Gansner, E. R. The Hillman-Grassl correspondence and the enumeration of reverse plane partitions MathSciNet:0607040
[3] Gansner, E. R. The enumeration of plane partitions via the Burge correspondence MathSciNet:0630832
[4] Krattenthaler, C. Generating functions for plane partitions of a given shape MathSciNet:1072987

Code

def statistic(T):
    m = 0
    for i, row in enumerate(T):
        try:
            m += row[i]
        except IndexError:
            break
    return m

Created

Nov 29, 2013 at 23:28 by Christian Krattenthaler

Updated

Aug 09, 2019 at 12:47 by Martin Rubey