PolyominoIdeals : Table of Contents

• PolyominoIdeals -- a package to work with collections of cells, polyominoes and associated binomial ideals
  • CollectionOfCells -- Type representing a collection of cells
  • cellCollection -- Create a collection of cells
  • polyoVertices -- Vertices of a collection of cells
  • polyoMatrix -- Matrix attached to a collection of cells
  • polyoMatrixReduced -- Reduced form of the polyomino matrix
  • innerInterval -- Inner interval of a collection of cells
  • polyoIdeal -- Ideal of inner 2-minors of a collection of cells
  • polyoToric -- Toric ideal of a polyomino
  • polyoLattice -- Lattice associated with a collection of cells
  • adjacent2MinorIdeal -- Ideal generated by adjacent 2-minors
  • isNonAttackingRooks -- Check if a rook configuration is non-attacking
  • allNonAttackingRookConfigurations -- All non-attacking rook configurations in Q
  • rookPolynomial -- Rook polynomial of a collection of cells
  • rookNumber -- Rook number of a collection of cells
  • equivalenceClassesSwitchingRook -- Equivalence classes of rook configurations under switching
  • switchingRookPolynomial -- Switching rook polynomial of a collection of cells
  • standardRookNumber -- Standard rook number of a collection of cells
  • standardNonAttackingRookConfigurations -- Standard non-attacking rook configurations
  • standardRookPolynomial -- Standard rook polynomial of a collection of cells
  • isPalindromic -- Check if a polynomial is palindromic
  • randomCollectionWithFixedRank -- Random collection of cells with fixed rank
  • randomCollectionOfCells -- Random collection of cells up to a given size
  • randomPolyominoWithFixedRank -- Random polyomino with fixed rank
  • randomPolyomino -- Random polyomino with random size up to a given bound
  • cellGraph -- Graph associated with a collection of cells
  • collectionIsConnected -- Check if a collection of cells is connected
  • connectedComponentsCells -- Connected components of a collection of cells
  • isRowConvex -- Row convexity of a collection of cells
  • isColumnConvex -- Column convexity of a collection of cells
  • isConvex -- Convexity of a collection of cells
  • collectionIsSimple -- Simplicity of a collection of cells
  • rankCollection -- Rank of a collection of cells
  • Field -- optional argument for polyoIdeal and adjacent2MinorIdeal
  • TermOrder -- optional argument for polyoIdeal and adjacent2MinorIdeal
  • RingChoice -- optional argument for polyoIdeal