polyoMatrixReduced -- Reduced form of the polyomino matrix

Usage:

polyoMatrixReduced Q
Inputs:
- Q, a collection of cells
Outputs:
- the reduced form of the polyomino matrix obtained by switching rows and columns as described in [HH1999]

Description

It returns the reduced form of the polyomino matrix by appropriately switching rows and columns, as explained in the reference below:

[HH1999] Koszul bipartite graphs, H. Ohsugi and T. Hibi, Adv. Appl. Math. 22 (1999), 25–28.

i1 : Q = cellCollection {{1,1},{2,2}};

i2 : M = polyoMatrix Q

o2 = | 0       x_(2,3) x_(3,3) |
     | x_(1,2) x_(2,2) x_(3,2) |
     | x_(1,1) x_(2,1) 0       |

                                                          3                                                   3
o2 : Matrix (QQ[x   , x   , x   , x   , x   , x   , x   ])  <-- (QQ[x   , x   , x   , x   , x   , x   , x   ])
                 3,3   3,2   2,3   2,2   2,1   1,2   1,1             3,3   3,2   2,3   2,2   2,1   1,2   1,1

i3 : N = polyoMatrixReduced Q

o3 = | x_(1,1) 0       x_(2,1) |
     | 0       x_(3,3) x_(2,3) |
     | x_(1,2) x_(3,2) x_(2,2) |

                                                          3                                                   3
o3 : Matrix (QQ[x   , x   , x   , x   , x   , x   , x   ])  <-- (QQ[x   , x   , x   , x   , x   , x   , x   ])
                 3,3   3,2   2,3   2,2   2,1   1,2   1,1             3,3   3,2   2,3   2,2   2,1   1,2   1,1

Ways to use polyoMatrixReduced:

polyoMatrixReduced(CollectionOfCells)

For the programmer

The object polyoMatrixReduced is a method function with options.

The source of this document is in PolyominoIdeals.m2:1169:0.

polyoMatrixReduced -- Reduced form of the polyomino matrix

Description

See also

Ways to use polyoMatrixReduced:

For the programmer