All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Page 1

Displaying 1 – 18 of 18

Showing per page

Determinant Representations of Sequences: A Survey

A. R. Moghaddamfar, S. Navid Salehy, S. Nima Salehy (2014)

Special Matrices

This is a survey of recent results concerning (integer) matrices whose leading principal minors are well-known sequences such as Fibonacci, Lucas, Jacobsthal and Pell (sub)sequences. There are different ways for constructing such matrices. Some of these matrices are constructed by homogeneous or nonhomogeneous recurrence relations, and others are constructed by convolution of two sequences. In this article, we will illustrate the idea of these methods by constructing some integer matrices of this...

Determinants of matrices associated with incidence functions on posets

Shaofang Hong, Qi Sun (2004)

Czechoslovak Mathematical Journal

Let S = { x 1 , ⋯ , x n } be a finite subset of a partially ordered set P . Let f be an incidence function of P . Let [ f ( x i ∧ x j ) ] denote the n × n matrix having f evaluated at the meet x i ∧ x j of x i and x j as its i , j -entry and [ f ( x i ∨ x j ) ] denote the n × n matrix having f evaluated at the join x i ∨ x j of x i and x j as its i , j -entry. The set S is said to be meet-closed if x i ∧ x j ∈ S for all 1 ≤ i , j ≤ n . In this paper we get explicit combinatorial formulas for the determinants of matrices [ f ( x i ∧ x j ) ] and [ f ( x i ∨ x j ) ] on any meet-closed set S . We also obtain necessary and sufficient conditions for the matrices...

Determining Integer-Valued Polynomials From Their Image

Vadim Ponomarenko (2010)

Actes des rencontres du CIRM

This note summarizes a presentation made at the Third International Meeting on Integer Valued Polynomials and Problems in Commutative Algebra. All the work behind it is joint with Scott T. Chapman, and will appear in [2]. Let Int ( ℤ ) represent the ring of polynomials with rational coefficients which are integer-valued at integers. We determine criteria for two such polynomials to have the same image set on ℤ .

Distributional properties of powers of matrices

Fernando Chamizo, Dulcinea Raboso (2014)

Czechoslovak Mathematical Journal

We apply the larger sieve to bound the number of 2 × 2 matrices not having large order when reduced modulo the primes in an interval. Our motivation is the relation with linear recursive congruential generators. Basically our results establish that the probability of finding a matrix with large order modulo many primes drops drastically when a certain threshold involving the number of primes and the order is exceeded. We also study, for a given prime and a matrix, the existence of nearby non-similar...

Currently displaying 1 – 18 of 18

Page 1