@@ -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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- def franklin_glaisher (self , s ):
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+ def glaisher_franklin (self , s ):
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r"""
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- Apply the Franklin- Glaisher bijection to ``self``.
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+ 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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EXAMPLES::
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- sage: Partition([4, 3, 2, 2, 1]).franklin_glaisher (2)
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+ 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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The map preserves the size::
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- sage: all(mu.franklin_glaisher (s).size() == n
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+ 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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- sage: l = [[mu.franklin_glaisher (s)
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+ sage: l = [[mu.glaisher_franklin (s)
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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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sage: all(len(set(ls)) == len(ls) for ls in l)
@@ -2526,14 +2526,14 @@ def franklin_glaisher(self, s):
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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)
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- sage: all(d(mu, s) == r(mu.franklin_glaisher (s), s)
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+ 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)
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....: for s in range(1, 5))
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True
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For `s=2`, the map is known to findstat::
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- sage: findmap(Partitions, lambda mu: mu.franklin_glaisher (2)) # optional - internet
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+ sage: findmap(Partitions, lambda mu: mu.glaisher_franklin (2)) # optional - internet
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0: Mp00312 (quality [100])
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"""
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s = ZZ (s )
@@ -2551,9 +2551,9 @@ def franklin_glaisher(self, s):
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P = self .parent ()
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return P .element_class (P , sorted (mu , reverse = True ))
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- def franklin_glaisher_inverse (self , s ):
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+ def glaisher_franklin_inverse (self , s ):
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r"""
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- Apply the inverse of the Franklin- Glaisher bijection to ``self``.
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+ Apply the inverse of the Glaisher-Franklin bijection to ``self``.
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INPUT:
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@@ -2569,23 +2569,23 @@ def franklin_glaisher_inverse(self, s):
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EXAMPLES::
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- sage: Partition([4, 3, 2, 2, 1]).franklin_glaisher (2)
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+ 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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- sage: Partition([3, 2, 2, 1, 1, 1, 1, 1]).franklin_glaisher_inverse (2)
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+ sage: Partition([3, 2, 2, 1, 1, 1, 1, 1]).glaisher_franklin_inverse (2)
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[4, 3, 2, 2, 1]
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TESTS:
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- The map is inverse to :meth:`franklin_glaisher `::
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+ The map is inverse to :meth:`glaisher_franklin `::
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- sage: all(mu.franklin_glaisher (s).franklin_glaisher_inverse (s) == mu
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+ sage: all(mu.glaisher_franklin (s).glaisher_franklin_inverse (s) == mu
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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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For `s=2`, the map is known to findstat::
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- sage: findmap(Partitions, lambda mu: mu.franklin_glaisher_inverse (2)) # optional - internet
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+ sage: findmap(Partitions, lambda mu: mu.glaisher_franklin_inverse (2)) # optional - internet
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0: Mp00313 (quality [100])
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"""
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s = ZZ (s )
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