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Permutations gives each distinct permutation once, as WMA does - #2087
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Permutations[{a, b, b}] listed {a, b, b} twice: permutations were taken
by position. WMA gives the permutations that differ as lists, in the
order of their first positional occurrence. Building only those also
keeps Combinatorica's ListGraphs[6, 3] from asking for all 15! orderings
of a 0/1 vector (455 distinct), which ran out of memory.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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Found while running the examples of Skiena and Pemmaraju's Computational Discrete Mathematics with the Combinatorica package and comparing every result with WMA 15.
Permutations[{a, b, b}]listed{a, b, b}twice, because permutations were taken by position. WMA gives the permutations that differ as lists, in the order of their first positional occurrence:Only the distinct ones are built now. This keeps Combinatorica's
ListGraphs[6, 3]from asking for all 15! orderings of a 0/1 vector, which ran out of memory; it has 455 distinct ones. Elements are told apart withSameQ, so1and1.stay different, as in WMA. The doc example that showed the duplicates is updated.All the fixes from this series together, merged on one branch: full pytest 4336 passed, 0 failed; doctests 4679 passed, 0 failed.
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