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Award ID contains: 2007891

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  1. ; ; (, Canadian Journal of Mathematics)
    Full Text Available 
  2. ; ; (, Proceedings of the annual ACMSIAM Symposium on Discrete Algorithms)
    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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    Accepted Manuscript Full Text Available
  3. (, Open Problem in Algebraic Combinatorics)
    In this survey we discuss the notion of combinatorial interpretation in the context of Algebraic Combinatorics and related areas. We approach the subject from the Computational Complexity perspective. We review many examples, state a workable definition, discuss many open problems, and present recent results on the subject. 
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    Accepted Manuscript Full Text Available
  4. ; (, Annual Symposium on Foundations of Computer Science)
    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. 
    more » « less
    Accepted Manuscript Full Text Available
  5. ; ; (, Combinatorica)
    We prove log-concavity of exit probabilities of lattice random walks in certain planar regions. 
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    Full Text Available 
  6. (, Seminaire lotharingien de combinatoire)
    Accepted Manuscript Full Text Available