Two new symmetric inseparable double squares

A method for constructing symmetric Hamiltonian double Latin squares

Symmetric squares of graphs

We consider symmetric powers of a graph. In particular, we show that the spectra of the symmetric square of strongly regular graphs with the same parameters are equal. We also provide some bounds on the spectra of the symmetric squares of more general graphs. The connection with generic exchange Hamiltonians in quantum mechanics is discussed in an appendix.

Two Recursively Inseparable Problems for Probabilistic Automata

This paper introduces and investigates decision problems for numberless probabilistic automata, i.e. probabilistic automata where the support of each probabilistic transitions is specified, but the exact values of the probabilities are not. A numberless probabilistic automaton can be instantiated into a probabilistic automaton by specifying the exact values of the non-zero probabilistic transit...

Irreducibility of Tensor Squares, Symmetric Squares and Alternating Squares

We investigate the question when the tensor square, the alternating square, or the symmetric square of an absolutely irreducible projective representation V of an almost simple group G is again irreducible. The knowledge of such representations is of importance in the description of the maximal subgroups of simple classical groups of Lie type. We show that if G is of Lie type in odd characteris...

Hamiltonian double latin squares

A double latin square of order 2n on symbols s1;y; sn is a 2n 2n matrix A 1⁄4 ðaijÞ in which each aij is one of the symbols s1;y; sn and each sk occurs twice in each row and twice in each column. For k 1⁄4 1;y; n let BðA; skÞ be the bipartite graph with vertices r1;y; r2n; c1;y; c2n and 4n edges 1⁄2ri; cj corresponding to ordered pairs ði; jÞ such that aij 1⁄4 sk: We say that A is Hamiltonian i...