We study quantum automorphism groups of vertex-transitive graphs having less than 11 vertices. With one possible exception, these can be obtained from cyclic groups Zn, symmetric groups Sn and quantum symmetric groups Qn, by using various product operations. The exceptional case is that of the Petersen graph, and we present some questions about it.

We study quantum automorphism groups of vertex-transitive graphs having less than 11 vertices. With one possible exception, these can be obtained from cyclic groups Zn , symmetric groups Sn and quantum symmetric groups Qn , by using various product operations. The exceptional case is that of the Petersen graph, and we present some questions about it.

For any graded poset P, we define a new graded poset, E(P ), whose elements are the edges in the Hasse diagram of P. For any group, G, acting on the boolean algebra, Bn, we conjecture that E(Bn/G) is Peck. We prove that the conjecture holds for “common cover transitive” actions. We give some infinite families of common cover transitive actions and show that the common cover transitive actions a...

A construction is given for an infinite family {0n} of finite vertex-transitive non-Cayley graphs of fixed valency with the property that the order of the vertex-stabilizer in the smallest vertex-transitive group of automorphisms of 0n is a strictly increasing function of n. For each n the graph is 4-valent and arc-transitive, with automorphism group a symmetric group of large prime degree p> 2...

in this paper, we investigate the existence of a positive solution of fully fuzzy linear equation systems. this paper mainly to discuss a new decomposition of a nonsingular fuzzy matrix, the symmetric times triangular (st) decomposition. by this decomposition, every nonsingular fuzzy matrix can be represented as a product of a fuzzy symmetric matrix s and a fuzzy triangular matrix t.

We study quantum automorphism groups of vertex-transitive graphs having less than 11 vertices. With one possible exception, these can be obtained from cyclic groups Zn, symmetric groups Sn and quantum symmetric groups Qn, by using various product operations. The exceptional case is that of the Petersen graph, and we present some questions about it.

We study quantum automorphism groups of vertex-transitive graphs having less than 11 vertices. With one possible exception, these can be obtained from cyclic groups Zn, symmetric groups Sn and quantum symmetric groups Qn, by using various product operations. The exceptional case is that of the Petersen graph, and we present some questions about it.

When the isotypic subspaces of a representation are viewed as the eigenspaces of a symmetric linear transformation, isotypic projections may be achieved as eigenspace projections and computed using the Lanczos iteration. In this paper, we show how this approach gives rise to an efficient isotypic projection method for permutation representations of distance transitive graphs and the symmetric g...