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Combinatorial equivalence of (0, 1) circulant matrices

1969
*
Journal of computer and system sciences (Print)
*

In this paper various properties

doi:10.1016/s0022-0000(69)80004-8
fatcat:j2tbwakk6fe43hh5cz7greqfdm
*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*. ...##
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Circulant weighing matrices

2010
*
Cryptography and Communications
*

We employ theoretical and computational techniques to construct new weighing

doi:10.1007/s12095-010-0025-z
fatcat:2khbfa26znacbat5uijqafhscq
*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*. ...##
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Graphs with circulant adjacency matrices

1970
*
Journal of Combinatorial Theory
*

Properties

doi:10.1016/s0021-9800(70)80068-0
fatcat:ksoketj6xzbkrfepuoryrxdksu
*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 ...##
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Circulant q-Butson Hadamard matrices
[article]

2017
*
arXiv
*
pre-print

We use algebraic number theory to prove a strong constraint on the dimension

arXiv:1701.08871v2
fatcat:3eikj6rjundahfyjug334kla6u
*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. ...##
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Factoring Matrices into the Product of Circulant and Diagonal Matrices

2015
*
Journal of Fourier Analysis and Applications
*

A generic matrix A ∈ C n×n is shown to be the product

doi:10.1007/s00041-015-9395-0
fatcat:hykrsoqtbrc2rekfinr5xm5hsa
*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 ]. ...##
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The inverses of some circulant matrices

2015
*
Applied Mathematics and Computation
*

In particular, we recover the inverses

doi:10.1016/j.amc.2015.08.084
fatcat:4myiwkxznndmbfvnyfgh2ggvem
*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. ...##
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Circulant matrices and mathematical juggling

2018
*
The Art of Discrete and Applied Mathematics
*

*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 ...

##
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The Binary Rank of Circulant Block Matrices
[article]

2022
*
arXiv
*
pre-print

rank by no more than the maximum

arXiv:2204.08942v1
fatcat:d6te7fl5ibfx5kn6wsjdymajma
*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. ...##
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Small circulant complex Hadamard matrices of Butson type
[article]

2014
*
arXiv
*
pre-print

We study the

arXiv:1311.5390v4
fatcat:wpbovnuvgffjtphhuaiqd23ahi
*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. ...##
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The inverse matrix of some circulant matrices
[article]

2015
*
arXiv
*
pre-print

In particular, we recover the inverses

arXiv:1505.07598v1
fatcat:rq43ebfkyffybfq5f3ffdmgisq
*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. ...##
###
Circulant weighing matrices of weight 22t

2006
*
Designs, Codes and Cryptography
*

In this paper, we prove the nonexistence

doi:10.1007/s10623-006-0026-2
fatcat:nmmijcjte5fyfn6mbnpojewnk4
*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. ...##
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Circulant matrices and Galois-Togliatti systems
[article]

2018
*
arXiv
*
pre-print

The goal

arXiv:1808.08387v1
fatcat:rau3br6ncndtrd72e53yptfepa
*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 ...##
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The geometry of an interchange: Minimal matrices and circulants

1997
*
Linear Algebra and its Applications
*

As a by-product, the interchange distance between a special

doi:10.1016/s0024-3795(97)80020-1
fatcat:akvj3u6ewnhinnevnan4qpjipe
*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. ...##
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Partial geometric designs having circulant concurrence matrices
[article]

2022
*
arXiv
*
pre-print

A partial geometry has two concurrences

arXiv:2106.11047v3
fatcat:etcnmlghsbgzbfim2dh3lsnodm
*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*. ...##
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The Geometry of an Interchange: Minimal Matrices and Circulants

1997
*
Linear Algebra and its Applications
*

As a by-product, the interchange distance between a special

doi:10.1016/s0024-3795(96)00465-x
fatcat:2pxsue73pbd2pnxjqqlbut44hq
*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. ...
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