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src/sage/combinat/partition.py

Lines changed: 14 additions & 14 deletions
Original file line numberDiff line numberDiff line change
@@ -2485,9 +2485,9 @@ def conjugate(self):
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par = Partitions_n(sum(self))
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return par.element_class(par, conjugate(self))
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2488-
def franklin_glaisher(self, s):
2488+
def glaisher_franklin(self, s):
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r"""
2490-
Apply the Franklin-Glaisher bijection to ``self``.
2490+
Apply the Glaisher-Franklin bijection to ``self``.
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INPUT:
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@@ -2502,21 +2502,21 @@ def franklin_glaisher(self, s):
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25032503
EXAMPLES::
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2505-
sage: Partition([4, 3, 2, 2, 1]).franklin_glaisher(2)
2505+
sage: Partition([4, 3, 2, 2, 1]).glaisher_franklin(2)
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[3, 2, 2, 1, 1, 1, 1, 1]
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TESTS:
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25102510
The map preserves the size::
25112511
2512-
sage: all(mu.franklin_glaisher(s).size() == n
2512+
sage: all(mu.glaisher_franklin(s).size() == n
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....: for n in range(20) for mu in Partitions(n)
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....: for s in range(1, 5))
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True
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The map is bijective::
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2519-
sage: l = [[mu.franklin_glaisher(s)
2519+
sage: l = [[mu.glaisher_franklin(s)
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....: for n in range(20) for mu in Partitions(n)]
25212521
....: for s in range(1, 5)]
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sage: all(len(set(ls)) == len(ls) for ls in l)
@@ -2526,14 +2526,14 @@ def franklin_glaisher(self, s):
25262526
25272527
sage: d = lambda la, s: set(p / s for p in la if p % s == 0)
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sage: r = lambda la, s: set(p for p in la if list(la).count(p) >= s)
2529-
sage: all(d(mu, s) == r(mu.franklin_glaisher(s), s)
2529+
sage: all(d(mu, s) == r(mu.glaisher_franklin(s), s)
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....: for n in range(20) for mu in Partitions(n)
25312531
....: for s in range(1, 5))
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True
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For `s=2`, the map is known to findstat::
25352535
2536-
sage: findmap(Partitions, lambda mu: mu.franklin_glaisher(2)) # optional - internet
2536+
sage: findmap(Partitions, lambda mu: mu.glaisher_franklin(2)) # optional - internet
25372537
0: Mp00312 (quality [100])
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"""
25392539
s = ZZ(s)
@@ -2551,9 +2551,9 @@ def franklin_glaisher(self, s):
25512551
P = self.parent()
25522552
return P.element_class(P, sorted(mu, reverse=True))
25532553

2554-
def franklin_glaisher_inverse(self, s):
2554+
def glaisher_franklin_inverse(self, s):
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r"""
2556-
Apply the inverse of the Franklin-Glaisher bijection to ``self``.
2556+
Apply the inverse of the Glaisher-Franklin bijection to ``self``.
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25582558
INPUT:
25592559
@@ -2569,23 +2569,23 @@ def franklin_glaisher_inverse(self, s):
25692569
25702570
EXAMPLES::
25712571
2572-
sage: Partition([4, 3, 2, 2, 1]).franklin_glaisher(2)
2572+
sage: Partition([4, 3, 2, 2, 1]).glaisher_franklin(2)
25732573
[3, 2, 2, 1, 1, 1, 1, 1]
2574-
sage: Partition([3, 2, 2, 1, 1, 1, 1, 1]).franklin_glaisher_inverse(2)
2574+
sage: Partition([3, 2, 2, 1, 1, 1, 1, 1]).glaisher_franklin_inverse(2)
25752575
[4, 3, 2, 2, 1]
25762576
25772577
TESTS:
25782578
2579-
The map is inverse to :meth:`franklin_glaisher`::
2579+
The map is inverse to :meth:`glaisher_franklin`::
25802580
2581-
sage: all(mu.franklin_glaisher(s).franklin_glaisher_inverse(s) == mu
2581+
sage: all(mu.glaisher_franklin(s).glaisher_franklin_inverse(s) == mu
25822582
....: for n in range(20) for mu in Partitions(n)
25832583
....: for s in range(1, 5))
25842584
True
25852585
25862586
For `s=2`, the map is known to findstat::
25872587
2588-
sage: findmap(Partitions, lambda mu: mu.franklin_glaisher_inverse(2)) # optional - internet
2588+
sage: findmap(Partitions, lambda mu: mu.glaisher_franklin_inverse(2)) # optional - internet
25892589
0: Mp00313 (quality [100])
25902590
"""
25912591
s = ZZ(s)

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