Abstract Two matrices $$H_1$$ H 1 and $$H_2$$ 2 with entries from a multiplicative group G are said to be monomially equivalent, denoted by $$H_1\cong H_2$$ ≅ , if one of the can obtained other via sequence row co...

We derive expressions for the average distance distributions in several ensembles of regular low-density parity-check codes (LDPC). Among these ensembles are the standard one defined by matrices having given column and row sums, ensembles defined by matrices with given column sums or given row sums, and an ensemble defined by bipartite graphs.

In 1981, G. D. James proved two theorems about the decomposition matrices of Schur algebras involving the removal of the first row or column from a Young diagram. He established corresponding results for the symmetric group using the Schur functor. We apply James’ techniques to prove that row removal induces an injection on the corresponding Ext between simple modules for the Schur algebra. We ...

The n Birkhoff polytope is the set of all doubly stochastic n × n matrices, that is, those matrices with nonnegative real coefficients in which every row and column sums to one. A wide open problem concerns the volumes of these polytopes, which have been known for n ≤ 8. We present a new, complex-analytic way to compute the Ehrhart polynomial of the Birkhoff polytope, that is, the function coun...

We consider the problem of structure prediction for sparse LU factorization with partial pivoting. In this context, it is well known that the column elimination tree plays an important role for matrices satisfying an irreducibility condition, called the strong Hall property. Our primary goal in this paper is to address the structure prediction problem for matrices satisfying a weaker assumption...

We present a results about convergence of products of row-stochastic matrices which are infinite to the left and all have positive diagonals. This is regarded as in inhomogeneous consensus process where confidence weights may change in every time step but where each agent has a little bit of self confidence. The positive diagonal leads to a fixed zero pattern in certain subproducts of the infin...

The eccentricity matrix E(G) of a connected graph G is obtained from the distance by keeping largest nonzero entries in each row and column, leaving zeros remaining ones. eigenvalues are E-eigenvalues G. In this article, we find inertia matrices trees. Interestingly, any tree on more than 4 vertices with odd diameter has exactly two positive negative (irrespective structure tree). Also, show th...