Related papers: Circuits and circulant minors
This paper derives a differential contraction condition for the existence of an orbitally-stable limit cycle in an autonomous system. This transverse contraction condition can be represented as a pointwise linear matrix inequality (LMI),…
McConnell [FOCS 2001] presented a flipping transformation from circular-arc graphs to interval graphs with certain patterns of representations. Beyond its algorithmic implications, this transformation is instrumental in identifying all…
Circulant graphs are a widely studied family of graphs whose members possess varying amounts of symmetry. Although considerable progress has been made in finding the automorphism groups of circulant graphs under certain restrictions, a…
From a generalization to $Z^n$ of the concept of congruence we define a family of regular digraphs or graphs called multidimensional circulants, which turn out to be Cayley (di)graphs of Abelian groups. This paper is mainly devoted to show…
We develop a theory of minors for alternating dimaps --- orientably embedded digraphs where, at each vertex, the incident edges (taken in the order given by the embedding) are directed alternately into, and out of, the vertex. We show that…
A circulant (di)graph is a (di)graph on n vertices that admits a cyclic automorphism of order n. This paper provides a survey of the work that has been done on finding the automorphism groups of circulant (di)graphs, including the…
We show that almost all circulant graphs have automorphism groups as small as possible. Of the circulant graphs that do not have automorphism group as small as possible, we give some families of integers such that it is not true that almost…
We give an "excluded minor" and a "structural" characterization of digraphs D that have the property that for every subdigraph H of D, the maximum number of disjoint circuits in H is equal to the minimum cardinality of a subset T of V(H)…
This short paper presents characterisations of normal arc-transitive circulants and arc-transitive normal circulants, that is, for a connected arc-transitive circulant $\Gamma=\Cay(C,S)$, it is shown that 1. Aut(C,S) is transitive on S if…
In this paper we investigate the theory of $a$-contraction with shifts with the intention of extending it to intermediate families. The theory of $a$-contraction with shifts is used to prove orbital $L^2$ stability to shock solutions of…
The present paper focuses on the construction of a set of submatrices of a circulant matrix such that it is a smaller set to verify that the circulant matrix is an MDS (maximum distance separable) one, comparing to the complete set of…
Given two sets $A$ and $B$ of integers, we consider the problem of finding a set $S \subseteq A$ of the smallest possible cardinality such the greatest common divisor of the elements of $S \cup B$ equals that of those of $A \cup B$. The…
We describe combinatorial properties of the defining row of a circulant Hadamard matrix by exploiting its orthogonality to subsequent rows, and show how to exclude several particular forms of these matrices.
Given a circulant matrix $\mathrm{circ}(c,a,0,0,...,0,a)$, $a\ne 0$, of order~$n$, we ``border'' it from left and from above by constant column and row, respectively, and we set the left top entry to be $-nc$. This way we get a~particular…
A compound determinant identity for minors of rectangular matrices is established. As an application, we derive Vandermonde type determinant formulae for classical group characters.
All matrices we consider have entries in a fixed algebraically closed field $K$. A minor of a square matrix is principal means it is defined by the same row and column indices. We study the ideal generated by size $t$ principal minors of a…
We evaluate determinants of "spiral" matrices, which are matrices in which entries are spiralling from the centre of the matrices towards the outside, with prescribed increments from one entry to the next depending on whether one moves…
Working on the set covering polyhedron of consecutive ones circulant matrices, Argiroffo and Bianchi found a class of facet defining inequalities, induced by a particular family of circulant minors. In this work we extend these results to…
An invariant theoretic characterization of subdiscriminants of matrices is given. The structure as a module over the special orthogonal group of the minimal degree non-zero homogeneous component of the vanishing ideal of the variety of real…
A number field K is a finite extension of rational number field Q. A circulant digraph integral over K means that all its eigenvalues are algebraic integers of K. In this paper we give the sufficient and necessary condition for circulant…