Related papers: On the complexity of computing Kronecker coefficie…
In this paper we study a max-min $k$-partition problem on a weighted graph, that could model a robust $k$-coalition formation. We settle the computational complexity of this problem as complete for class $\Sigma_2^P$. This hardness holds…
This paper is a contribution to the investigation of closed partition relations for pairs of countable ordinals. As our main result, we prove that \[\omega^4 \cdot (n-2)+1 < R^{cl}(\omega \cdot n+1,3)<\omega^5\] for every integer $n \geq…
The computational complexity of optimum decoding for an orthogonal space-time block code G satisfying the orthogonality property that the Hermitian transpose of G multiplied by G is equal to a constant c times the sum of the squared symbols…
We prove explicit congruences modulo powers of arbitrary primes for three smallest parts functions: one for partitions, one for overpartitions, and one for partitions without repeated odd parts. The proofs depend on $\ell$-adic properties…
The combinatorial properties of partitions with various restrictions on their hooksets are explored. A connection with numerical semigroups extends current results on simultaneous s/t-cores. Conditions that suffice for a partition to…
We prove that the Hadwiger number of an $n$-vertex graph $G$ (the maximum size of a clique minor in $G$) cannot be computed in time $n^{o(n)}$, unless the Exponential Time Hypothesis (ETH) fails. This resolves a well-known open question in…
We study the problem of partitioning a given simple polygon $P$ into a minimum number of connected polygonal pieces, each of bounded size. We describe a general technique for constructing such partitions that works for several notions of…
The Kronecker coefficients are the decomposition multiplicities of the tensor product of two irreducible representations of the symmetric group. Unlike the Littlewood--Richardson coefficients, which are the analogues for the general linear…
Using $P(n,m)$, the number of integer partitions of $n$ into exactly $m$ parts, which was the subject of an earlier paper, $P(n,m,p)$, the number of integer partitions of $n$ into exactly $m$ parts with each part at most $p$, can be…
Graph partitioning schedules parallel calculations like sparse matrix-vector multiply (SpMV). We consider contiguous partitions, where the $m$ rows (or columns) of a sparse matrix with $N$ nonzeros are split into $K$ parts without…
We show that approximating the trace norm contraction coefficient of a quantum channel within a constant factor is NP-hard. Equivalently, this shows that determining the optimal success probability for encoding a bit in a quantum system…
The Kronecker product of two Schur functions $s_{\mu}$ and $s_{\nu}$, denoted by $s_{\mu}*s_{\nu}$, is the Frobenius characteristic of the tensor product of the irreducible representations of the symmetric group corresponding to the…
We give an introduction to some of the recent ideas that go under the name "geometric complexity theory". We first sketch the proof of the known upper and lower bounds for the determinantal complexity of the permanent. We then introduce the…
We prove an $\Omega(n^{1-1/k} \log k \ /2^k)$ lower bound on the $k$-party number-in-hand communication complexity of collision-finding. This implies a $2^{n^{1-o(1)}}$ lower bound on the size of tree-like cutting-planes proofs of the bit…
Quantum contextuality is a limitation on deterministic hidden variable models, testable in measurement scenarios where outcomes differ under quantum or classical descriptions due to a common set of constraints. When considering measurements…
The best deterministic unconditionally proven integer factorization algorithms have exponential running time complexities of O(N^(1/4)) arithmetic operations, and conditional on the Riemann hypothesis, there is a deterministic algorithm of…
For primes $\ell$ and nonnegative integers $a$, we study the partition functions $$p_\ell(a;n):= \#\{\lambda \vdash n : \text{ord}_\ell(H(\lambda))=a\},$$ where $H(\lambda)$ denotes the product of hook lengths of a partition $\lambda$.…
We point out that the remarkable Knutson and Tao Saturation Theorem and polynomial time algorithms for LP have together an important and immediate consequence in Geometric Complexity Theory. The problem of deciding positivity of…
We present a criterion for multiplicity-freeness of the decomposition of the restriction Res$^G_H(\rho_1 \otimes \rho_2)$ of the Kronecker product of two generic irreducible representations $\rho_1, \rho_2$ of a finite group $G$ with…
The computational complexity of the Maximum Likelihood decoding algorithm in [1], [2] for orthogonal space-time block codes is smaller than specified.