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combinat[firstpart] - first partition in canonical partition sequence
combinat[nextpart] - next partition in canonical partition sequence
combinat[lastpart] - last partition in canonical partition sequence
combinat[prevpart] - previous partition in canonical partition sequence
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Calling Sequence
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firstpart(n)
nextpart(l)
lastpart(n)
prevpart(l)
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Parameters
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l
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partition; non-decreasing list of positive integers
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n
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positive integer
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Description
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All four of the functions use the canonical partition sequence defined by combinat[encodepart].
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Given a positive integer n, firstpart(n) computes and returns the first partition of n in the canonical partition sequence.
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Given a partition l of n, nextpart(l) computes and returns the next partition of n in the canonical partition sequence.
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Given a positive integer n, lastpart(n) computes and returns the last partition of n in the canonical partition sequence.
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Given a partition l of n, prevpart(l) computes and returns the previous partition of n in the canonical partition sequence.
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Examples
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![[[1, 1, 1], [1, 2], [3]]](/support/helpjp/helpview.aspx?si=7021/file03548/math119.png)
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![[1, 1, 1]](/support/helpjp/helpview.aspx?si=7021/file03548/math126.png)
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![nextpart([1, 1, 1])](/support/helpjp/helpview.aspx?si=7021/file03548/math130.png)
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![[1, 2]](/support/helpjp/helpview.aspx?si=7021/file03548/math133.png)
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![nextpart([1, 2])](/support/helpjp/helpview.aspx?si=7021/file03548/math137.png)
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![[3]](/support/helpjp/helpview.aspx?si=7021/file03548/math140.png)
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![prevpart([3])](/support/helpjp/helpview.aspx?si=7021/file03548/math144.png)
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![[1, 2]](/support/helpjp/helpview.aspx?si=7021/file03548/math147.png)
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![[3]](/support/helpjp/helpview.aspx?si=7021/file03548/math154.png)
| (6) |
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