#### Filter Results:

#### Publication Year

2012

2016

#### Publication Type

#### Co-author

#### Key Phrase

#### Publication Venue

Learn More

We prove that in the geometric complexity theory program the vanishing of rectangular Kronecker coefficients cannot be used to prove superpolynomial determinantal complexity lower bounds for the permanent polynomial. Moreover, we prove the positivity of rectangular Kronecker coefficients for a large class of partitions where the side lengths of the… (More)

We study multiplication of any Schubert polynomial S w by a Schur polynomial s λ (the Schubert polynomial of a Grassmannian permutation) and the expansion of this product in the ring of Schubert polynomials. We derive explicit nonnegative combinatorial expressions for the expansion coefficients for certain special partitions λ, including hooks and the 2 × 2… (More)

The permanent versus determinant conjecture is a major problem in complexity theory that is equivalent to the separation of the complexity classes VPws and VNP. Mulmuley and Sohoni [34] suggested to study a strengthened version of this conjecture over the complex numbers that amounts to separating the orbit closures of the determinant and padded permanent… (More)

We study the complexity of computing Kronecker coefficients $${g(\lambda,\mu,\nu)}$$ g ( λ , μ , ν ) . We give explicit bounds in terms of the number of parts $${\ell}$$ ℓ in the partitions, their largest part size N and the smallest second part M of the three partitions. When M = O(1), i.e., one of the partitions is hook-like, the bounds are linear in log… (More)

- Joel Brewster Lewis, Yan Zhang, Nan Li, Steven Sam, Greta Panova, Dorian Croitoru +2 others
- 2012

We consider a variety of questions related to pattern avoidance in alternating permutations and generalizations thereof. We give bijective enumerations of alternating permutations avoiding patterns of length 3 and 4, of permutations that are the reading words of a " thickened staircase " shape (or equivalently of permutations with descent set {k, 2k, 3k,. .… (More)

- ‹
- 1
- ›