ferrers diagrams造句

• Partitions can be graphically visualized with Young diagrams or Ferrers diagrams.
• Another representation for plane partitions is in the form of Ferrers diagrams.
• Another representation for solid partitions is in the form of Ferrers diagrams.
• The largest elements whose Ferrers diagrams are rectangular that lie under the staircase are these:
• Consider the Ferrers diagram of any partition of " n " into distinct parts.
• Of the " n " th triangular number has a Ferrers diagram that looks like a staircase.
• This holds for every term " except " when the process cannot be performed on every Ferrers diagram with n dots.
• The idea is to start with the Ferrers diagram of b and shift ones to the right until the column sums are a.
• This division of centered hexagonal arrays gives generalized pentagonal numbers as trapezoidal arrays, which may be interpreted as Ferrers diagrams for their partition.
• This enables us to pair off Ferrers diagrams contributing 1 and & minus; 1 to the " x n " term of the series, resulting in a net coefficient of 0.
• A "'Young diagram "'( also called Ferrers diagram, particularly when represented using dots ) is a finite collection of boxes, or cells, arranged in left-justified rows, with the row lengths in non-increasing order.
• In summary, it has been shown that partitions into an even number of distinct parts and an odd number of distinct parts exactly cancel each other, except if " n " is a generalized pentagonal number g _ k = k ( 3k-1 ) / 2, in which case there is exactly one Ferrers diagram left over.