Related papers: A New Generalized Cassini Determinant
The purpose of this paper is to compute the asymptotics of determinants of finite sections of operators that are trace class perturbations of Toeplitz operators. For example, we consider the asymptotics in the case where the matrices are of…
We prove an irreducibility criterion for polynomials with power series coefficients generalizing previous known results concerning quasi-ordinary polynomials.
We study the Jacobi-Trudi-type determinant which is conjectured to be the q-character of a certain, in many cases irreducible, finite-dimensional representation of the quantum affine algebra of type D_n. Unlike the A_n and B_n cases, a…
We establish some identities relating two sequences that are, as explained, related to the Tribonacci sequence. One of these sequences bears the same resemblance to the Tribonacci sequence as the Lucas sequence does to the Fibonacci…
In this paper, the determinants of $n\times n$ matrices over commutative finite chain rings and over commutative finite principal ideal rings are studied. The number of $n\times n$ matrices over a commutative finite chain ring ${R}$ of a…
To each associative unitary finite-dimensional algebra over a normal base, we associative a canonical multiplicative function called its determinant. We give various properties of this construction, as well as applications to the topology…
Based on a variant of Sury's polynomial identity we derive new expressions for various finite Fibonacci (Lucas) sums. We extend the results to Fibonacci and Chebyshev polynomials, and also to Horadam sequences. In addition to deriving sum…
In this paper, we investigate new class of sequences related to fully degenerate Bernoulli numbers and polynomials. From those sequences, we derive some formulae for the degenerate Bernoulli and Euler polynomials.
In a previous paper we have presented a partition formula for the even-index Fibonacci numbers using the preprojective representations of the 3-Kronecker quiver and its universal cover, the 3-regular star. Now we deal in a similar way with…
We improve the resolvent estimate in the Kreiss matrix theorem for a set of matrices that generate uniformly bounded semigroups. The new resolvent estimate is proved to be equivalent to Kreiss's resolvent condition, and it better describes…
In this work, we study the computational complexity of quantum determinants, a $q$-deformation of matrix permanents: Given a complex number $q$ on the unit circle in the complex plane and an $n\times n$ matrix $X$, the $q$-permanent of $X$…
We give an expression for the determinant of the twisted Laplacian associated with any linear representation of a finite quiver in terms of traces of the holonomy of its cycles. To establish this expression, we prove a general identity for…
We consider a new formula for Berezinian (superdeterminant). The Berezinian of a supermatrix $A$ is expressed as the ratio of polynomial invariants of $A$. This formula follows from recurrence relations existing for supertraces of exterior…
We prove new determinantal identities for a family of flagged Schur polynomials. As a corollary of these identities we obtain determinantal expressions of Schubert polynomials for certain vexillary permutations.
The article uses an arithmetic-geometric Fibonacci series to find the expected value of trials needed to observe k consecutive successes for the first time in a Bernoulli experiment using a recurrence relation. It is important to note that…
We give combinatorial proofs of $q$-Stirling identities using restricted growth words. This includes a poset theoretic proof of Carlitz's identity, a new proof of the $q$-Frobenius identity of Garsia and Remmel and of Ehrenborg's Hankel…
We study some properties of restricted and associated Fubini numbers. In particular, they have the natural extensions of the original Fubini numbers in the sense of determinants. We also introduce modified Bernoulli and Cauchy numbers and…
We derive new matrix representation for higher order Daehee numbers and polynomials, the higher order lambda-Daehee numbers and polynomials and the twisted lambda-Daehee numbers and polynomials of order k. This helps us to obtain simple and…
This study applies the binomial, k-binomial, rising k-binomial and falling k-binomial transforms to the modified k-Fibonacci-like sequence. Also, the Binet formulas and generating functions of the above mentioned four transforms are newly…
In this paper, we generalize Spencer's hyperbolic cosine algorithm to the matrix-valued setting. We apply the proposed algorithm to several problems by analyzing its computational efficiency under two special cases of matrices; one in which…