We prove that deciding the vanishing of the character of the symmetric group is C=P-complete. We use this hardness result to prove that the square of the character is not contained in #P, unless the polynomial hierarchy collapses to the second level. This rules out the existence of any (unsigned) combinatorial description for the square of the characters. As a byproduct of our proof we conclude that deciding positivity of the character is PP-complete under many-one reductions, and hence PH-hard under Turing-reductions.
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What we've lost by closing our labs - and what we risk reopening them
- Award ID(s):
- 2041047
- PAR ID:
- 10273429
- Date Published:
- Journal Name:
- ASBMB today
- Volume:
- 19
- Issue:
- 6
- ISSN:
- 2372-0409
- Page Range / eLocation ID:
- 42-44
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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