Generalized Pascal triangles and Toeplitz matrices.
Graphs determined by their (signless) Laplacian spectra.
Hadamard product of GCD matrices.
Infinite divisibility of Smith matrices
Integer matrices related to Liouville's function
In this note, we construct some integer matrices with determinant equal to certain summation form of Liouville's function. Hence, it offers a possible alternative way to explore the Prime Number Theorem by means of inequalities related to matrices, provided a better estimate on the relation between the determinant of a matrix and other information such as its eigenvalues is known. Besides, we also provide some comparisons on the estimate of the lower bound of the smallest singular value. Such discussion...
Inversion of incidence mappings.
Jacobsthal numbers and alternating sign matrices.
Keys and alternating sign matrices.
Linear discrepancy of basic totally unimodular matrices.
Lower bounds for the largest eigenvalue of the gcd matrix on
Consider the matrix with ’th entry . Its largest eigenvalue and sum of entries satisfy . Because cannot be expressed algebraically as a function of , we underestimate it in several ways. In examples, we compare the bounds so obtained with one another and with a bound from S. Hong, R. Loewy (2004). We also conjecture that for all . If is large enough, this follows from F. Balatoni (1969).
Matrices and submatrices with constrained invariant factors
Matrix problems and stable homotopy types of polyhedra
This is a survey of the results on stable homotopy types of polyhedra of small dimensions, mainly obtained by H.-J. Baues and the author [3, 5, 6]. The proofs are based on the technique of matrix problems (bimodule categories).
Matrix representable so-rings.
Maximising the permanent of -matrices and the number of extensions of Latin rectangles.
Meixner-type results for Riordan arrays and associated integer sequences.
More on evaluating determinants
Multiple gcd-closed sets and determinants of matrices associated with arithmetic functions
Let f be an arithmetic function and S = {x1, …, xn} be a set of n distinct positive integers. By (f(xi, xj)) (resp. (f[xi, xj])) we denote the n × n matrix having f evaluated at the greatest common divisor (xi, xj) (resp. the least common multiple [xi, xj]) of x, and xj as its (i, j)-entry, respectively. The set S is said to be gcd closed if (xi, xj) ∈ S for 1 ≤ i, j ≤ n. In this paper, we give formulas for the determinants of the matrices (f(xi, xj)) and (f[xi, xj]) if S consists of multiple coprime...
Netted matrices.
New families of integer matrices whose leading principal minors form some well-known sequences.
Nonexistence results for Hadamard-like matrices.