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Supplementary Eulerian vectors in isotropic systems

Bill Jackson
<span title="">1991</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/g6u5fful5vcr3a7gppc6y47el4" style="color: black;">Journal of combinatorial theory. Series B (Print)</a> </i> &nbsp;
The vector A is said to be an Eulerian vector of S if it is complete and r(A, S) = 0. It follows from [B2, Lemma 4 .11 that every isotropic system has two supplementary Eulerian vectors.  ...  [B2, Lemma 4.11 , Bouchet showed that for any complete vector BE K ', the isotropic system S = (L, V) has an Eulerian vector supplementary to B.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0095-8956(91)90055-o">doi:10.1016/0095-8956(91)90055-o</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/drnj3robqzhyjftbv2wxsdf5lm">fatcat:drnj3robqzhyjftbv2wxsdf5lm</a> </span>
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Graphic presentations of isotropic systems

André Bouchet
<span title="">1988</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/g6u5fful5vcr3a7gppc6y47el4" style="color: black;">Journal of combinatorial theory. Series B (Print)</a> </i> &nbsp;
Isotropic systems are structures which unify some properties common to 4-regular graphs and pairs of dual binary matroids. We study the representation of isotroic systems by simple graphs.  ...  FIGURE 1 1 4 . 4 EULERIAN VECTORS AND FUNDAMENTAL BASES An eulerian vector of an isotropic system S = (L, V) is a complete vector A E K" such that r(A) = 0.  ...  ProoJ Let us choose two supplementary vectors A and BE K", and let us consider the isotropic system S= (AN+ BN', V).  ... 
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Tutte-martin polynomials and orienting vectors of isotropic systems

André Bouchet
<span title="">1991</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/yxooi3wjmbgqtbp7l4evjeuj4i" style="color: black;">Graphs and Combinatorics</a> </i> &nbsp;
For this purpose we introduce the orienting vectors of an isotropic system in order to generalize the eulerian orientations of 4-regular graphs.  ...  Isotropic systems are structures which unify some properties of 4-regular graphs and of pairs of dual binary matroids.  ...  Where Isotropic systems have been introduced in [2, 3] in order to unify some properties of 4-regular graphs and binary matroids.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/bf01787630">doi:10.1007/bf01787630</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/osoituca6raxhb67bzvizyctpi">fatcat:osoituca6raxhb67bzvizyctpi</a> </span>
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Isotropic Systems

André Bouchet
<span title="">1987</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/54t3hgai4fhhthc74mj7z7tapu" style="color: black;">European journal of combinatorics (Print)</a> </i> &nbsp;
In this paper we introduce a combinatorial and algebraic structure called isotropic system.  ...  The introduction of the paper describes the applications of isotropic systems that we have found at present and which will be developed in subsequent papers.  ...  ( 4 . 2 ) 42 If M = (N, V) and M* = (N L , V) are dual binary matroids and A and Bare supplementary vectors of K V , then (AN + BN L , V) is an isotropic system.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0195-6698(87)80027-6">doi:10.1016/s0195-6698(87)80027-6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2zpwybasw5aynod6mwtb6y5w7y">fatcat:2zpwybasw5aynod6mwtb6y5w7y</a> </span>
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A characterisation of graphs having three pairwise compatible Euler tours

Bill Jackson
<span title="">1991</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/g6u5fful5vcr3a7gppc6y47el4" style="color: black;">Journal of combinatorial theory. Series B (Print)</a> </i> &nbsp;
Two Euler tours of a graph G are compatible if no pair of adjacent edges of G are consecutive in both tours.  ...  In [J2] we characterised the isotropic systems which contain three pairwise supplementary Eulerian vectors. THEOREM 2.1. Let S = (L, V) be an isotropic system.  ...  Let S = (L, V) be a partial isotropic system. The rank of A in S is defined as r(A, S) = dim(a n L). The vector A is said to be an Eulerian vector of S if it is complete and r(A) = 0.  ... 
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Page 2389 of Mathematical Reviews Vol. , Issue 93e [page]

<span title="">1993</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Jaroslav Nesetfil (CS-CHRL) 93e:05063 05C45 05B35 Jackson, Bill (4-LNDG) Supplementary Eulerian vectors in isotropic systems. J. Combin. Theory Ser. B 53 (1991), no. 1, 93-105.  ...  The present paper gives a solution of the corresponding abstract prob- lem, which is to characterize the isotropic systems having three pairwise supplementary Eulerian vectors.  ... 
<span class="external-identifiers"> </span>
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Recognizing locally equivalent graphs

André Bouchet
<span title="">1993</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/civgv5utqzhu7aj6voo6vc5vx4" style="color: black;">Discrete Mathematics</a> </i> &nbsp;
(2.1) If (F, A, B) is a graphic presentation of an isotropic system S, then A is an Eulerian vector of S.  ...  If A and A' are any two Eulerian vectors of an isotropic system S=(L, V), then there exists a word m on V such that A' = A * m. (2.4) Let P = (F, A, B) be a graphic presentation of an isotropic system  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0012-365x(93)90357-y">doi:10.1016/0012-365x(93)90357-y</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hl7xh3favfecxm3pv2foiwgmwy">fatcat:hl7xh3favfecxm3pv2foiwgmwy</a> </span>
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Isotropic systems and the interlace polynomial [article]

Joanna A. Ellis-Monaghan, Irasema Sarmiento
<span title="2006-07-07">2006</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Through a series of papers in the 1980's, Bouchet introduced isotropic systems and the Tutte-Martin polynomial of an isotropic system.  ...  isotropic systems.  ...  By Theorem 2.9, given a simple graph G on the vertex set V , supplementary vectors A and B of K V , and L = {A(N(P )) + B(P ) : P ∈ P(V )}, then the pair S = (L, V ) is an isotropic system.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/0606641v2">arXiv:math/0606641v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/m2p3u336jnf25ovgo3bsth6pom">fatcat:m2p3u336jnf25ovgo3bsth6pom</a> </span>
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Prime vertex-minors of a prime graph [article]

Donggyu Kim, Sang-il Oum
<span title="2022-02-16">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
A vertex v of a graph is non-essential if at least two of the three kinds of vertex-minor reductions at v result in prime graphs.  ...  vertices has at least 3 non-essential vertices if and only if it is not locally equivalent to a graph with two specified vertices x and y consisting of at least two internally-disjoint paths from x to y in  ...  Let S be an isotropic system. For every complete vector c, there is an Eulerian vector a of S supplementary to c. Proposition 3.7 (Bouchet [3, (4.3 ) and (4.4)]).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2202.07877v1">arXiv:2202.07877v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wx2tesnwxnhkjdwdlonla3hbku">fatcat:wx2tesnwxnhkjdwdlonla3hbku</a> </span>
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Rank-Width and Well-Quasi-Ordering

Sang-il Oum
<span title="">2008</span> <i title="Society for Industrial &amp; Applied Mathematics (SIAM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/hn6wut4eynat5my6xdfsebg7fm" style="color: black;">SIAM Journal on Discrete Mathematics</a> </i> &nbsp;
The proof uses the notion of isotropic systems defined by Bouchet.  ...  We prove another theorem of this kind in terms of rank-width and vertexminors.  ...  This work was performed while the author was at the Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey and partially supported by the SRC program of Korea Science  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/050629616">doi:10.1137/050629616</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dfypq474zbatxoph7im6pfe3ty">fatcat:dfypq474zbatxoph7im6pfe3ty</a> </span>
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General magnetic dipolar interaction of spin-spin coupled molecular dimers. Application to an EPR spectrum of xanthine oxidase

R. E. Coffman, G. R. Buettner
<span title="">1979</span> <i title="American Chemical Society (ACS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/tilntgzzvvhrfe5m6tjk2fuw2u" style="color: black;">The Journal of Physical Chemistry</a> </i> &nbsp;
MezSnClZ-pyridine complexes is proven in the latter system. Little has been reported about the former complex.  ...  The formation constant of the 1:l complex in the MezSnClz + 2,2'-bipyridine system is 4500 k 320 dm2 mol-' in CHCl,CHCl" about twice as large as that reported in CH,CN, and reflects much weaker solvation  ...  Lowe for several manuscripts and preprints, and for their helpful and encouraging correspondence concerning the nature of the long-range spin-spin interactions in xanthine oxidase and xanthine dehydrogenase  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1021/j100481a018">doi:10.1021/j100481a018</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7pdgk4ymijh37dziyoudowuxiy">fatcat:7pdgk4ymijh37dziyoudowuxiy</a> </span>
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Acoustic Birefringence via Non-Eulerian Metamaterials [article]

Farzad Zangeneh-Nejad, Romain Fleury
<span title="2018-03-24">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
This is achieved in a suitably designed acoustic metamaterial which is non-Eulerian, in the sense that at low frequencies, it cannot be homogenized to a uniform acoustic medium whose behavior is characterized  ...  Thanks to the feasibility of engineering its subwavelength structure, such non-Eulerian metamaterial allows one to desirably manipulate the birefringence process.  ...  Non-Eulerian metamaterials The metamaterial we investigate in the following is represented in Fig. 1a .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1803.09070v1">arXiv:1803.09070v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bqsqnilim5a47j2deuskydiqjm">fatcat:bqsqnilim5a47j2deuskydiqjm</a> </span>
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Well-quasi-ordering of matrices under Schur complement and applications to directed graphs

Mamadou Moustapha Kanté
<span title="">2012</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/54t3hgai4fhhthc74mj7z7tapu" style="color: black;">European journal of combinatorics (Print)</a> </i> &nbsp;
We extend in this way the notion of representability of delta-matroids by Bouchet.  ...  We generalise this result to σ-symmetric matrices introduced by Rao and myself in [The Rank-Width of Edge-Coloured Graphs, arXiv:0709.1433v4].  ...  As for Tutte chain groups and isotropic systems, Lagrangian chain groups are vector spaces equipped with a bilinear form.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ejc.2012.03.034">doi:10.1016/j.ejc.2012.03.034</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/g3ivd3hytrcxjjwgsakwf3rzpq">fatcat:g3ivd3hytrcxjjwgsakwf3rzpq</a> </span>
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Vertex-minors, monadic second-order logic, and a conjecture by Seese

Bruno Courcelle, Sang-il Oum
<span title="">2007</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/g6u5fful5vcr3a7gppc6y47el4" style="color: black;">Journal of combinatorial theory. Series B (Print)</a> </i> &nbsp;
The proofs use isotropic systems.  ...  Acknowledgments This work has been initiated during the Dagstuhl seminar in May 2004. We thank the organizers, A. Brandstädt, D. Corneil, K. Jansen, and J. Spinrad for inviting us.  ...  (Bouchet [3]) Let S = (V , L) be an isotropic system. For every complete vector c of K V , there is an Eulerian vector a of S, supplementary to c. Proposition 4.2.  ... 
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Spatiotemporal velocity-velocity correlation function in fully developed turbulence

Léonie Canet, Vincent Rossetto, Nicolás Wschebor, Guillaume Balarac
<span title="2017-02-16">2017</span> <i title="American Physical Society (APS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5pgnwkvlevhybgsbuc3q7fchx4" style="color: black;">Physical review. E</a> </i> &nbsp;
Here, we provide a theoretical prediction for the space and time dependent velocity-velocity correlation function of homogeneous and isotropic turbulence from the field theory associated to Navier-Stokes  ...  This solution is compared to two-point two-times correlation functions computed in direct numerical simulations. We obtain a remarkable agreement both in the inertial and in the dissipative ranges.  ...  This would imply that the k −5/3 decay in wave-vector is related to a ω −2 decay in frequency (see Supplementary information), which is characteristic of velocities measured along the flow (Lagrangian  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physreve.95.023107">doi:10.1103/physreve.95.023107</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/28297914">pmid:28297914</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qa3md53cwndddiptgeruhjb2ne">fatcat:qa3md53cwndddiptgeruhjb2ne</a> </span>
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