In the present paper, we give upper and lower bounds for the spectral norm of g-circulant matrix, whose the rst row entries are the classical Horadam numbers U (a,b) i . In addition, we also establish an explicit formula of the spectral norm for g-circulant matrix with the rst row ([U (a,b) 0 ] , [U (a,b) 1 ] , · · · , [U (a,b) n−1 ]).

In this paper we rst review the basic computational properties of per-manents, and then address some problems concerning permanents of (0; 1) circulant matrices. In particular we analyze their role at the boundary between computational tractability and intractability, showing that (i) a generic circulant matrix contains large arbitrary submatrices, a fact which casts some doubt on the tractabil...

We show that if a Barker sequence of length n > 13 exists, then either n = 189 260 468 001 034 441 522 766 781 604, or n > 2 · 1030. This improves the lower bound on the length of a long Barker sequence by a factor of more than 107. We also show that all but fewer than 1600 integers n ≤ 4 ·1026 can be eliminated as the order of a circulant Hadamard matrix. These results are obtained by completi...

A framework for constructing circulant and block circulant preconditioners (C) for a symmetric linear system Ax= b arising from signal and image processing applications is presented in this paper. The proposed scheme does not make explicit use of matrix elements of A. It is ideal for applications in which A only exists in the form of a matrix vector multiplication routine, and in which the proc...

Binary embeddings provide efficient and powerful ways to perform operations on large scale data. However binary embedding typically requires long codes in order to preserve the discriminative power of the input space. Thus binary coding methods traditionally suffer from high computation and storage costs in such a scenario. To address this problem, we propose Circulant Binary Embedding (CBE) wh...

Calculating the permanent of a (0, 1) matrix is a #P -complete problem but there are some classes of structuredmatrices for which the permanent is calculable in polynomial time. The most well-known example is the fixed-jump (0, 1) circulant matrix which, using algebraic techniques, was shown by Minc to satisfy a constant-coefficient fixed-order recurrence relation. In this note we show how, by ...

Calculating the permanent of a (0, 1) matrix is a #P complete problem but there are some classes of structured matrices for which the permanent is calculable in polynomial time. The most well-known example is the fixed-jump (0, 1) circulant matrix which, using algebraic techniques, was shown by Minc to satisfy a constantcoefficient fixed-order recurrence relation. In this note we show how, by i...

We consider an asymptotic expansion of Kashaev’s invariant or of the colored Jones function for the torus link T (2, 2m). We shall give q-series identity related to these invariants, and show that the invariant is regarded as a limit of q being N -th root of unity of the Eichler integral of a modular form of weight 3/2 which is related to the ŝu(2)m−2 character.

We classify all circulant weighing matrices whose order and weight are products of powers of 2 and 3. In particular, we show that proper CW(v, 36)’s exist for all v ≡ 0 (mod 48), all of which are new.