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sage: bij.set_statistics((len, len), (alpha1, beta1), (alpha2, beta2))
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sage: a, b = bij.statistics_table()
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sage: table(a, header_row=True, frame=True)
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- +-----------+--------+--------+--------+
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- | a | α_1(a) | α_2(a) | α_3(a) |
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- +===========+========+========+========+
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- | [] | 0 | 0 | 0 |
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- +-----------+--------+--------+--------+
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- | [1] | 1 | 1 | 1 |
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- +-----------+--------+--------+--------+
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- | [1, 2] | 2 | 2 | 2 |
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- +-----------+--------+--------+--------+
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- | [2, 1] | 2 | 1 | 0 |
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- +-----------+--------+--------+--------+
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- | [1, 2, 3] | 3 | 3 | 3 |
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- +-----------+--------+--------+--------+
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- | [1, 3, 2] | 3 | 2 | 1 |
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- +-----------+--------+--------+--------+
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- | [2, 1, 3] | 3 | 2 | 1 |
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- +-----------+--------+--------+--------+
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- | [2, 3, 1] | 3 | 2 | 0 |
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- +-----------+--------+--------+--------+
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- | [3, 1, 2] | 3 | 1 | 0 |
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- +-----------+--------+--------+--------+
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- | [3, 2, 1] | 3 | 2 | 1 |
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- +-----------+--------+--------+--------+
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+ ┌───────────┬────────┬────────┬────────┐
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+ │ a | α_1(a) | α_2(a) | α_3(a) |
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+ ╞═══════════╪════════╪════════╪════════╡
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+ │ [] | 0 | 0 | 0 |
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+ ├───────────┼────────┼────────┼────────┤
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+ │ [1] | 1 | 1 | 1 |
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+ ├───────────┼────────┼────────┼────────┤
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+ │ [1, 2] | 2 | 2 | 2 |
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+ ├───────────┼────────┼────────┼────────┤
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+ │ [2, 1] | 2 | 1 | 0 |
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+ ├───────────┼────────┼────────┼────────┤
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+ │ [1, 2, 3] | 3 | 3 | 3 |
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+ ├───────────┼────────┼────────┼────────┤
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+ │ [1, 3, 2] | 3 | 2 | 1 |
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+ ├───────────┼────────┼────────┼────────┤
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+ │ [2, 1, 3] | 3 | 2 | 1 |
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+ ├───────────┼────────┼────────┼────────┤
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+ │ [2, 3, 1] | 3 | 2 | 0 |
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+ ├───────────┼────────┼────────┼────────┤
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+ │ [3, 1, 2] | 3 | 1 | 0 |
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+ ├───────────┼────────┼────────┼────────┤
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+ │ [3, 2, 1] | 3 | 2 | 1 |
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+ └───────────┴────────┴────────┴────────┘
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sage: table(b, header_row=True, frame=True)
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- +-----------+---+--------+--------+--------+
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- | b | τ | β_1(b) | β_2(b) | β_3(b) |
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- +===========+===+========+========+========+
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- | [] | 0 | 0 | 0 | 0 |
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- +-----------+---+--------+--------+--------+
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- | [1] | 1 | 1 | 1 | 1 |
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- +-----------+---+--------+--------+--------+
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- | [1, 2] | 2 | 2 | 1 | 0 |
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- +-----------+---+--------+--------+--------+
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- | [2, 1] | 1 | 2 | 2 | 2 |
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- +-----------+---+--------+--------+--------+
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- | [1, 2, 3] | 3 | 3 | 1 | 0 |
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- +-----------+---+--------+--------+--------+
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- | [1, 3, 2] | 2 | 3 | 2 | 1 |
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- +-----------+---+--------+--------+--------+
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- | [2, 1, 3] | 2 | 3 | 2 | 1 |
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- +-----------+---+--------+--------+--------+
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- | [2, 3, 1] | 2 | 3 | 2 | 1 |
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- +-----------+---+--------+--------+--------+
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- | [3, 1, 2] | 2 | 3 | 2 | 0 |
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- +-----------+---+--------+--------+--------+
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- | [3, 2, 1] | 1 | 3 | 3 | 3 |
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- +-----------+---+--------+--------+--------+
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+ ┌───────────┬───┬────────┬────────┬────────┐
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+ │ b | τ | β_1(b) | β_2(b) | β_3(b) |
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+ ╞═══════════╪═══╪════════╪════════╪════════╡
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+ │ [] | 0 | 0 | 0 | 0 |
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+ ├───────────┼───┼────────┼────────┼────────┤
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+ │ [1] | 1 | 1 | 1 | 1 |
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+ ├───────────┼───┼────────┼────────┼────────┤
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+ │ [1, 2] | 2 | 2 | 1 | 0 |
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+ ├───────────┼───┼────────┼────────┼────────┤
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+ │ [2, 1] | 1 | 2 | 2 | 2 |
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+ ├───────────┼───┼────────┼────────┼────────┤
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+ │ [1, 2, 3] | 3 | 3 | 1 | 0 |
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+ ├───────────┼───┼────────┼────────┼────────┤
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+ │ [1, 3, 2] | 2 | 3 | 2 | 1 |
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+ ├───────────┼───┼────────┼────────┼────────┤
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+ │ [2, 1, 3] | 2 | 3 | 2 | 1 |
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+ ├───────────┼───┼────────┼────────┼────────┤
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+ │ [2, 3, 1] | 2 | 3 | 2 | 1 |
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+ ├───────────┼───┼────────┼────────┼────────┤
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+ │ [3, 1, 2] | 2 | 3 | 2 | 0 |
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+ ├───────────┼───┼────────┼────────┼────────┤
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+ │ [3, 2, 1] | 1 | 3 | 3 | 3 |
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+ └───────────┴───┴────────┴────────┴────────┘
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sage: from sage.combinat.cyclic_sieving_phenomenon import orbit_decomposition
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sage: bij.set_constant_blocks(orbit_decomposition(A, rotate_permutation))
@@ -854,53 +854,53 @@ def statistics_table(self, header=True):
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sage: bij.set_statistics((wex, des), (fix, adj))
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sage: a, b = bij.statistics_table()
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sage: table(a, header_row=True, frame=True)
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- +-----------+--------+--------+
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- | a | α_1(a) | α_2(a) |
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- +===========+========+========+
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- | [] | 0 | 0 |
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- +-----------+--------+--------+
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- | [1] | 1 | 1 |
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- +-----------+--------+--------+
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- | [1, 2] | 2 | 2 |
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- +-----------+--------+--------+
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- | [2, 1] | 1 | 0 |
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- +-----------+--------+--------+
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- | [1, 2, 3] | 3 | 3 |
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- +-----------+--------+--------+
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- | [1, 3, 2] | 2 | 1 |
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- +-----------+--------+--------+
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- | [2, 1, 3] | 2 | 1 |
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- +-----------+--------+--------+
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- | [2, 3, 1] | 2 | 0 |
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- +-----------+--------+--------+
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- | [3, 1, 2] | 1 | 0 |
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- +-----------+--------+--------+
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- | [3, 2, 1] | 2 | 1 |
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- +-----------+--------+--------+
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+ ┌───────────┬────────┬────────┐
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+ │ a | α_1(a) | α_2(a) |
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+ ╞═══════════╪════════╪════════╡
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+ │ [] | 0 | 0 |
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+ ├───────────┼────────┼────────┤
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+ │ [1] | 1 | 1 |
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+ ├───────────┼────────┼────────┤
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+ │ [1, 2] | 2 | 2 |
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+ ├───────────┼────────┼────────┤
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+ │ [2, 1] | 1 | 0 |
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+ ├───────────┼────────┼────────┤
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+ │ [1, 2, 3] | 3 | 3 |
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+ ├───────────┼────────┼────────┤
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+ │ [1, 3, 2] | 2 | 1 |
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+ ├───────────┼────────┼────────┤
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+ │ [2, 1, 3] | 2 | 1 |
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+ ├───────────┼────────┼────────┤
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+ │ [2, 3, 1] | 2 | 0 |
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+ ├───────────┼────────┼────────┤
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+ │ [3, 1, 2] | 1 | 0 |
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+ ├───────────┼────────┼────────┤
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+ │ [3, 2, 1] | 2 | 1 |
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+ └───────────┴────────┴────────┘
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sage: table(b, header_row=True, frame=True)
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- +-----------+---+--------+--------+
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- | b | τ | β_1(b) | β_2(b) |
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- +===========+===+========+========+
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- | [] | 0 | 0 | 0 |
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- +-----------+---+--------+--------+
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- | [1] | 1 | 1 | 1 |
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- +-----------+---+--------+--------+
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- | [1, 2] | 2 | 1 | 0 |
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- +-----------+---+--------+--------+
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- | [2, 1] | 1 | 2 | 2 |
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- +-----------+---+--------+--------+
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- | [1, 2, 3] | 3 | 1 | 0 |
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- +-----------+---+--------+--------+
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- | [1, 3, 2] | 2 | 2 | 1 |
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- +-----------+---+--------+--------+
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- | [2, 1, 3] | 2 | 2 | 1 |
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- +-----------+---+--------+--------+
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- | [2, 3, 1] | 2 | 2 | 1 |
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- +-----------+---+--------+--------+
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- | [3, 1, 2] | 2 | 2 | 0 |
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- +-----------+---+--------+--------+
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- | [3, 2, 1] | 1 | 3 | 3 |
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- +-----------+---+--------+--------+
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+ ┌───────────┬───┬────────┬────────┐
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+ │ b | τ | β_1(b) | β_2(b) |
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+ ╞═══════════╪═══╪════════╪════════╡
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+ │ [] | 0 | 0 | 0 |
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+ ├───────────┼───┼────────┼────────┤
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+ │ [1] | 1 | 1 | 1 |
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+ ├───────────┼───┼────────┼────────┤
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+ │ [1, 2] | 2 | 1 | 0 |
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+ ├───────────┼───┼────────┼────────┤
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+ │ [2, 1] | 1 | 2 | 2 |
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+ ├───────────┼───┼────────┼────────┤
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+ │ [1, 2, 3] | 3 | 1 | 0 |
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+ ├───────────┼───┼────────┼────────┤
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+ │ [1, 3, 2] | 2 | 2 | 1 |
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+ ├───────────┼───┼────────┼────────┤
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+ │ [2, 1, 3] | 2 | 2 | 1 |
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+ ├───────────┼───┼────────┼────────┤
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+ │ [2, 3, 1] | 2 | 2 | 1 |
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+ ├───────────┼───┼────────┼────────┤
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+ │ [3, 1, 2] | 2 | 2 | 0 |
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+ ├───────────┼───┼────────┼────────┤
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+ │ [3, 2, 1] | 1 | 3 | 3 |
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+ └───────────┴───┴────────┴────────┘
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TESTS:
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@@ -911,29 +911,29 @@ def statistics_table(self, header=True):
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sage: bij = Bijectionist(A, B, tau)
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sage: a, b = bij.statistics_table()
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sage: table(a, header_row=True, frame=True)
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- +--------+
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- | a |
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- +========+
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- | [] |
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- +--------+
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- | [1] |
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- +--------+
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- | [1, 2] |
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- +--------+
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- | [2, 1] |
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- +--------+
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+ ┌────────┐
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+ │ a |
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+ ╞════════╡
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+ │ [] |
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+ ├────────┤
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+ │ [1] |
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+ ├────────┤
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+ │ [1, 2] |
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+ ├────────┤
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+ │ [2, 1] |
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+ └────────┘
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sage: table(b, header_row=True, frame=True)
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- +--------+---+
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- | b | τ |
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- +========+===+
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- | [] | 0 |
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- +--------+---+
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- | [1] | 1 |
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- +--------+---+
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- | [1, 2] | 2 |
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- +--------+---+
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- | [2, 1] | 1 |
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- +--------+---+
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+ ┌────────┬───┐
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+ │ b | τ |
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+ ╞════════╪═══╡
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+ │ [] | 0 |
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+ ├────────┼───┤
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+ │ [1] | 1 |
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+ ├────────┼───┤
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+ │ [1, 2] | 2 |
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+ ├────────┼───┤
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+ │ [2, 1] | 1 |
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+ └────────┴───┘
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We can omit the header::
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