augmentFilling -- append an entry to a column of a Filling

Usage:

augmentFilling(T, c, e)
Inputs:
- T, an instance of the type Filling,
- c, an integer, column index
- e, an integer, entry to append
Outputs:
- an instance of the type Filling, a new filling where e has been appended to the bottom of column c, or (if c >= #T) a new rightmost column {e} has been created

Description

This is the natural cell-adding operation for Schur-functor combinatorics: extending a filling by one cell at the bottom of column $c$ (or creating a new rightmost column if $c$ is past the current rightmost column). It is the building block used to describe Schur-module maps by their action on tableaux; see for example the Koszul-style differential built in the example of schurModulesMap.

i1 : T = new Filling from {{0,1}, {1}}

     +-+-+
o1 = |0|1|
     |1| |
     +-+-+

o1 : Filling

i2 : T

     +-+-+
o2 = |0|1|
     |1| |
     +-+-+

o2 : Filling

i3 : augmentFilling(T, 0, 2)

     +-+-+
o3 = |0|1|
     |1| |
     |2| |
     +-+-+

o3 : Filling

i4 : augmentFilling(T, 1, 2)

     +-+-+
o4 = |0|1|
     |1|2|
     +-+-+

o4 : Filling

i5 : augmentFilling(T, 5, 3)

     +-+-+-+
o5 = |0|1|3|
     |1| | |
     +-+-+-+

o5 : Filling

Ways to use augmentFilling:

augmentFilling(Filling,ZZ,ZZ)

For the programmer

The object augmentFilling is a method function.

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/SchurFunctors.m2:1528:0.

augmentFilling -- append an entry to a column of a Filling

Description

See also

Ways to use augmentFilling:

For the programmer