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Lah Numbers
In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ..., the Lah numbers, discovered by Ivo Lah in 1954, are coefficients expressing rising factorials in terms of falling factorials. They are also the coefficients of the nth derivatives of e^. Unsigned Lah numbers have an interesting meaning in combinatorics: they count the number of ways a Set (mathematics), set of ''n'' elements can be Partition of a set, partitioned into ''k'' nonempty linearly ordered subsets. Lah numbers are related to Stirling numbers. Unsigned Lah numbers : : L(n,k) = \frac. Signed Lah numbers : : L'(n,k) = (-1)^n \frac. ''L''(''n'', 1) is always ''n''!; in the interpretation above, the only partition of into 1 set can have its set ordered in 6 ways: :, , , , or ''L''(3, 2) corresponds ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lah Numbers
In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ..., the Lah numbers, discovered by Ivo Lah in 1954, are coefficients expressing rising factorials in terms of falling factorials. They are also the coefficients of the nth derivatives of e^. Unsigned Lah numbers have an interesting meaning in combinatorics: they count the number of ways a Set (mathematics), set of ''n'' elements can be Partition of a set, partitioned into ''k'' nonempty linearly ordered subsets. Lah numbers are related to Stirling numbers. Unsigned Lah numbers : : L(n,k) = \frac. Signed Lah numbers : : L'(n,k) = (-1)^n \frac. ''L''(''n'', 1) is always ''n''!; in the interpretation above, the only partition of into 1 set can have its set ordered in 6 ways: :, , , , or ''L''(3, 2) corresponds ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
