A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Filters
Combinatorial equivalence of (0, 1) circulant matrices
1969
Journal of computer and system sciences (Print)
Preserved Fulltext
In this paper various properties of (0, 1) square matrices are investigated, and in particular, circulant matrices are considered. ...
If r is a (0, 1) vector or code word of length n and contains exactly K one elements, then let A(r) be the corresponding circulant matrix having r as its first row. ...
BACKGROUND Tucker [5] has formulated the following concept of combinatorial equivalence of matrices. ...
doi:10.1016/s0022-0000(69)80004-8
fatcat:j2tbwakk6fe43hh5cz7greqfdm
Circulant weighing matrices
2010
Cryptography and Communications
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
We employ theoretical and computational techniques to construct new weighing matrices constructed from two circulants. ...
In particular, we construct W (148, 144), W (152, 144), W (156, 144) which are listed as open in the second edition of the Handbook of Combinatorial Designs. ...
The above definition of disjoint support for arbitrary matrices (i.e. not necessarily circulant) boils down to the Definition 4 of disjoint support for circulant matrices. ...
doi:10.1007/s12095-010-0025-z
fatcat:2khbfa26znacbat5uijqafhscq
Graphs with circulant adjacency matrices
1970
Journal of Combinatorial Theory
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
Properties of a graph (directed or undirected) whose adjacency matrix is a circulant are studied. ...
Two different criteria are given under which two graphs with circulant adjacency matrices are isomorphic if and only if their connection sets are multiplicatively related. ...
OPEN PROBLEMS The theorems of this paper have given only a partial description of pairs of graphs with circulant adjacency matrices for which isomorphism is equivalent to having equivalent connection sets ...
doi:10.1016/s0021-9800(70)80068-0
fatcat:ksoketj6xzbkrfepuoryrxdksu
Circulant q-Butson Hadamard matrices
[article]
2017
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
We use algebraic number theory to prove a strong constraint on the dimension of a circulant q-Butson Hadamard matrix when d = p^m and then explicitly construct a family of examples in all possible dimensions ...
These results relate to the long-standing circulant Hadamard matrix conjecture in combinatorics. ...
Circulant q-BH matrices of dimension d are equivalent to δ-fibrous functions f : Z/(d) → Z/(q). Theorem 3. Let q = p n be a prime power and ζ a primitive qth root of unity. ...
arXiv:1701.08871v2
fatcat:3eikj6rjundahfyjug334kla6u
Factoring Matrices into the Product of Circulant and Diagonal Matrices
2015
Journal of Fourier Analysis and Applications
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
A generic matrix A ∈ C n×n is shown to be the product of circulant and diagonal matrices with the number of factors being 2n − 1 at most. ...
For the linear factors, the sum of two PD matrices is factored into the product of two diagonal matrices and a circulant matrix. ...
Although the notion of permutation equivalence is graph theoretically nonstandard, combinatorial linear algebraically it is perfectly natural [2, p. 4 ]. ...
doi:10.1007/s00041-015-9395-0
fatcat:hykrsoqtbrc2rekfinr5xm5hsa
The inverses of some circulant matrices
2015
Applied Mathematics and Computation
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
In particular, we recover the inverses of some well known circulant matrices whose coefficients are arithmetic or geometric sequences, Horadam numbers among others. ...
We present here necessary and sufficient conditions for the invertibility of circulant and symmetric matrices that depend on three parameters and moreover, we explicitly compute the inverse. ...
Notice that Circ b(2, −1, 0) is nothing but the so called combinatorial Laplacian of a n-cycle. ...
doi:10.1016/j.amc.2015.08.084
fatcat:4myiwkxznndmbfvnyfgh2ggvem
Circulant matrices and mathematical juggling
2018
The Art of Discrete and Applied Mathematics
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Circulants form a well-studied and important class of matrices, and they arise in many algebraic and combinatorial contexts, in particular as multiplication tables of cyclic groups and as special classes ...
Schroeder) 1 If t i = 0, then there is no ball to toss at time i. c b This work is licensed under http://creativecommons.org/licenses/by/3.0/ ...
In Section 3, we elaborate on the connection between juggling sequences and circulant matrices as discussed in [3] , and relate juggling sequences to the permanent of circulants defined in terms of n ...
doi:10.26493/2590-9770.1235.c68
fatcat:mammjnt2ibgxjh5cudpmuahja4
The Binary Rank of Circulant Block Matrices
[article]
2022
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is application/pdf.
rank by no more than the maximum of (n_i,k_i)-1 over all i ∈ [m]. ...
Using this method, we prove that the binary rank of the complement of a (k_1, ..., k_m ; n_1, ..., n_m) circulant block diagonal matrix for integers satisfying n_i>k_i>0 for each i ∈ [m] exceeds its real ...
Equivalently, it is the smallest size of a partition of the ones in M into monochromatic combinatorial rectangles. ...
arXiv:2204.08942v1
fatcat:d6te7fl5ibfx5kn6wsjdymajma
Small circulant complex Hadamard matrices of Butson type
[article]
2014
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Note that this fulltext copy is not of the "primary" version of this work. The version it corresponds to is:
2014 pre-print arXiv:1311.5390v2 fatcat:whanpiuffreddbhhc5wuu5bg4aOther Versions
We study the circulant complex Hadamard matrices of order n whose entries are l-th roots of unity. ...
We then provide a list of equivalence classes of such matrices, for small values of n,l. ...
Shortly after we posted a question 2 which is a more elementary but equivalent statement of Theorem 5.1, Noam Elkies posted an answer to this question which is basically a proof of Theorem 5.1. ...
arXiv:1311.5390v4
fatcat:wpbovnuvgffjtphhuaiqd23ahi
The inverse matrix of some circulant matrices
[article]
2015
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
In particular, we recover the inverses of some well known circulant matrices whose coeffifficients are arithmetic or geometric sequences, Horadam numbers among others. ...
We present here necessary and sufficient conditions for the invertibility of circulant and symmetric matrices that depend on three parameters and moreover, we explicitly compute the inverse. ...
Notice that Circ b(2, −1, 0) is nothing but the so called combinatorial Laplacian of a n-cycle. ...
arXiv:1505.07598v1
fatcat:rq43ebfkyffybfq5f3ffdmgisq
Circulant weighing matrices of weight 22t
2006
Designs, Codes and Cryptography
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
In this paper, we prove the nonexistence of two weighing matrices of weight 81, namely CW (88, 81) and CW (99, 81). ...
By using zero-based indexing, we define n − 1} and N = {g i |W 0,i = −1, i = 0, 1 . . . , n − 1} , MSC(2010): Primary: 05C15; Secondary: 20D60. ...
A table of these matrices follows below along with the parameter values that would satisfy the hypothesis of Theorem 4.3. ...
doi:10.1007/s10623-006-0026-2
fatcat:nmmijcjte5fyfn6mbnpojewnk4
Circulant matrices and Galois-Togliatti systems
[article]
2018
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
The goal of this article is to compare the coefficients in the expansion of the permanent with those in the expansion of the determinant of a three-lines circulant matrix. ...
As an application we prove a conjecture concerning the minimality of Galois-Togliatti systems. ...
In this article, we are interested in the so-called r-lines circulant matrices, i.e. circulant matrices Circ(x 0 , x 1 . . . , x d−1 ) of order d > r, where d−r among x 0 , . . . , x d−1 are specialized ...
arXiv:1808.08387v1
fatcat:rau3br6ncndtrd72e53yptfepa
The geometry of an interchange: Minimal matrices and circulants
1997
Linear Algebra and its Applications
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
As a by-product, the interchange distance between a special circulant and the set of minimal matrices in its class is determined. Several open problems are stated. ...
A general method is given for constructing minimal matrices using circulants. ...
INTRODUCTION Two classes of combinatorial matrices are of special interest in what follows. ...
doi:10.1016/s0024-3795(97)80020-1
fatcat:akvj3u6ewnhinnevnan4qpjipe
Partial geometric designs having circulant concurrence matrices
[article]
2022
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is application/pdf.
Note that this fulltext copy is not of the "primary" version of this work. The version it corresponds to is:
2021 pre-print arXiv:2106.11047v2 fatcat:4ckmphus5reothrtubfavqtzyaOther Versions
A partial geometry has two concurrences 1 and 0 and a transversal design TD_λ(k, u) has two concurrences λ and 0. ...
In this paper, we show the existence of other partial geometric designs having two or three distinct concurrences, and investigate which symmetric circulant matrices are realized as the concurrence matrices ...
PGDs having circulant concurrence matrices We notice that the concurrence matrices of many PGDs are circulant. ...
arXiv:2106.11047v3
fatcat:etcnmlghsbgzbfim2dh3lsnodm
The Geometry of an Interchange: Minimal Matrices and Circulants
1997
Linear Algebra and its Applications
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
As a by-product, the interchange distance between a special circulant and the set of minimal matrices in its class is determined. Several open problems are stated. 0 Elsevier Science Inc., 1997 * ...
A general method is given for constructing minimal matrices using circulants. ...
INTRODUCTION Two classes of combinatorial matrices are of special interest in what follows. ...
doi:10.1016/s0024-3795(96)00465-x
fatcat:2pxsue73pbd2pnxjqqlbut44hq
« Previous
Showing results 1 — 15 out of 3,668 results