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Embedding Linkages on an Integer Lattice

Landau, Immerman
2002 Algorithmica  
We show that the question of determining whether a linkage can be embedded on the integer lattice is strongly N P -complete.  ...  can be placed on integer lattice points?  ...  Lenstra, Jr. for pointing out an error in an earlier version of this paper.  ... 
doi:10.1007/s00453-001-0087-6 fatcat:zsld35uqezfcndskci5vwuvojm

Page 6081 of Mathematical Reviews Vol. , Issue 96j [page]

1996 Mathematical Reviews  
Since the matrix C is an explicitly computable integer matrix, this allows one to answer the question in any special case.  ...  Let A be a linear transformation of R” which preserves the lattice [ (for example, if T is the standard integer lattice, A € GL(n,Z)).  ... 

Page 8521 of Mathematical Reviews Vol. , Issue 2002K [page]

2002 Mathematical Reviews  
|[Landau, Susan]; Immerman, N. (1-MA-C; Amherst, MA) Embedding linkages on an integer lattice. (English summary) Algorithmica 32 (2002), no. 3, 423-436.  ...  With the help of a reduction from 3-SAT it is shown that the question of determining whether a linkage can be embedded on the integer lattice is strongly NP- complete.  ... 

European Journal of Combinatorics Contents, Volume 26

2005 European journal of combinatorics (Print)  
., On the structure of k-connected graphs without K k -minor . . . . . 293 THOMAS, R. and WOLLAN, P., An improved linear edge bound for graph linkages . . . . . . . . . . . . . . . . . 309 NEGAMI, S.,  ...  classical Weyl groups: minimal chains and covering relation . . . . . . . . . . . . . . 729 DE OLIVEIRA, A.G. and E SILVA, D.O., Note on the integer geometry of bitwise XOR . . . . . . . . . . . . . .  ... 
doi:10.1016/s0195-6698(05)00128-9 fatcat:fb5uilehgvgzxgmj7sfw4lm5hq

Page 3032 of Mathematical Reviews Vol. , Issue 84h [page]

1984 Mathematical Reviews  
One of these linkages performs mechanically the inversion by reciprocal radii discussed in Chapter 8, but this is used only as an introduction to a number of fascinating problems involving linkages.  ...  Author’s summary: “We define the S-congruences on an algebra UeE‘Y, where V is a regular variety, by the condition 8EC,(U)= U/OEHSP(2,). We show that C,(U) is an algebraic lattice and C,(U)=[@ni,).  ... 

European Journal of Combinatorics Index, Volume 26

2005 European journal of combinatorics (Print)  
., An inequality for regular near polygons . . . . . . . . . . . . . . . . 227 THOMAS, R. and WOLLAN, P., An improved linear edge bound for graph linkages . . . . . . . . . . . . . . . . . 309 BEDNARSKA  ...  -N., Note sur les permutations minimales . . . . . . . 245 HARADA, M., KITAZUME, M., MUNEMASA, A. and VENKOV, B., On some self-dual codes and unimodular lattices in dimension 48 . . 543 HENKE, A., On p-Kostka  ... 
doi:10.1016/s0195-6698(05)00129-0 fatcat:vuytixhru5bupfpbxzzanswabu

Page 5332 of Mathematical Reviews Vol. , Issue 2001H [page]

2001 Mathematical Reviews  
Summary: “We study the primary decomposition of lattice basis ideals. These ideals are binomial ideals with generators given by the elements of a basis of a saturated integer lattice.  ...  Linkage is an important process in commutative algebra and alge- braic geometry.  ... 

What is a superrigid subgroup? [article]

Dave Witte Morris
2007 arXiv   pre-print
This is an expository paper. It is well known that a linear transformation can be defined to have any desired action on a basis.  ...  This is related to a very classical topic in geometry, the study of linkages.  ...  When the (1, 2)-entry t of an element of G is an integer, the (3, 3)-entry e 2πit is 1, so we see that H ⊂ G . In fact, it is not difficult to see that H is a lattice in G .  ... 
arXiv:0712.2299v1 fatcat:zanjpudujfcm5pgdpp2pb4bswa

Spatial Sorting Algorithms for Parallel Computing in Networks

Max OrHai, Christof Teuscher
2011 2011 Fifth IEEE Conference on Self-Adaptive and Self-Organizing Systems Workshops  
For insertion sort, we obtain these results without depending on any but statistical properties of the network medium.  ...  Many basic techniques in computer science have been founded on the assumption that physical computing resources are scarce but orderly, and that the cost of effective direct communication between physically  ...  But, if any two nodes in an existing linkage share a common inactive neighbor not already in the linkage, there is an opportunity for an alternative form of growth we call swelling.  ... 
doi:10.1109/sasow.2011.10 dblp:conf/saso/OrHaiT11 fatcat:lrf36exvcrecdnkjohlydxq2pe

Quantum Knots and Lattices, or a Blueprint for Quantum Systems that Do Rope Tricks [article]

Samuel J. Lomonaco, Louis H. Kauffman
2009 arXiv   pre-print
These three moves wiggle, wag, and tug generate a unitary group, called the lattice ambient group, which acts on the state space of the quantum system.  ...  To define a quantum knot system, we replace the standard three Reidemeister knot moves with an equivalent set of three moves, called respectively wiggle, wag, and tug, so named because they mimic how a  ...  In other words, the 4-bar linkage is a local move on a larger linkage. In particular, the 4-bar linkage gives an illustration of a local curvature move, taking place in a plane.  ... 
arXiv:0910.5891v1 fatcat:zdqtrajapfbgjhgooz2r5us5ou

Highly transitive representations of free groups and free products

A.M.W. Glass, Stephen H. McCleary
1991 Bulletin of the Australian Mathematical Society  
FAITHFULNESS AND LINKAGE. Let A be any (fc)-orbit in the right regular representation of H. The action of (h) on A is the regular representation (Z, Z) of the integers.  ...  Choose 6 here If a € T, we impose one more constraint on /?, namely that /? not differ by an integer from a or from either end of any previously defined 2-arrow (u G y ) .  ... 
doi:10.1017/s0004972700028744 fatcat:typvbzfnefbo3fnd5apryvs6vq

On the Form and Growth of Complex Crystals: The Case of Tsai-Type Clusters

Jean Taylor, Erin Teich, Pablo Damasceno, Yoav Kallus, Marjorie Senechal
2017 Symmetry  
We then present a revised description and possible growth model for one particular system of alloys, those containing Tsai-type clusters, that includes an important class of quasicrystals.  ...  Note the absence of the number 5 (and all integers greater than 6). Why? Let L be a plane lattice and φ X a 72 • rotation about a lattice point X.  ...  Note the absence of the number 5 (and all integers greater than 6). Why? Let L be a plane lattice and φX a 72° rotation about a lattice point X.  ... 
doi:10.3390/sym9090188 fatcat:y7pttu2azrhetoanrjeu7mk44i

Planar defect in approximant: the case of Cu-Al-Sc alloy [article]

Tsutomu Ishimasa, Yeong-Gi So, Marek Mihalkovič
2021 arXiv   pre-print
An atomic structure model of the planar defect has been constructed referring to the structural properties of the regular 1/1 approximant; namely truncated triacontahedron framework and embedded clusters  ...  This vector corresponds to a 6-dimensional translation of type [111000] and also to the c-linkage of Tsai-type clusters.  ...  Detailed research on such defects is an interesting subject for the future.  ... 
arXiv:2108.03341v2 fatcat:z667ezuc5vaeph4bcd5tg5zney

Page 962 of Mathematical Reviews Vol. , Issue 82c [page]

1982 Mathematical Reviews  
is one and only one automorphism which maps x onto y.  ...  In this paper the author describes completely the cases in which a graph does not contain an (X,,X>,)),)2)-linkage. The same result was obtained (but stated without proof) by P. D.  ... 

Schemes supported on the singular locus of a hyperplane arrangement in P^n [article]

J. Migliore, U. Nagel, H. Schenck
2019 arXiv   pre-print
We show that for any positive integer r there is an arrangement A for which R/ J fails to be Cohen-Macaulay in only one degree, and this failure is by r; we also give an analogous result for √(J).  ...  Terao's conjecture says that freeness of A is determined by the combinatorics of the intersection lattice of A.  ...  of the incidence lattice.  ... 
arXiv:1908.03939v1 fatcat:o3duj5bus5h7vmy7lyifls7u4a
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