2,961 research outputs found
Isomorphy up to complementation
Considering uniform hypergraphs, we prove that for every non-negative integer
there exist two non-negative integers and with such that
two -uniform hypergraphs and on the same set
of vertices, with , are equal up to complementation whenever
and are -{hypomorphic up to complementation}.
Let be the least integer such that the conclusion above holds and
let be the least corresponding to . We prove that . In the special case or
, we prove that . The values and
were obtained in a previous work.Comment: 15 page
On a stronger reconstruction notion for monoids and clones
Motivated by reconstruction results by Rubin, we introduce a new
reconstruction notion for permutation groups, transformation monoids and
clones, called automatic action compatibility, which entails automatic
homeomorphicity. We further give a characterization of automatic
homeomorphicity for transformation monoids on arbitrary carriers with a dense
group of invertibles having automatic homeomorphicity. We then show how to lift
automatic action compatibility from groups to monoids and from monoids to
clones under fairly weak assumptions. We finally employ these theorems to get
automatic action compatibility results for monoids and clones over several
well-known countable structures, including the strictly ordered rationals, the
directed and undirected version of the random graph, the random tournament and
bipartite graph, the generic strictly ordered set, and the directed and
undirected versions of the universal homogeneous Henson graphs.Comment: 29 pp; Changes v1-->v2::typos corr.|L3.5+pf extended|Rem3.7 added|C.
Pech found out that arg of L5.3-v1 solved Probl2-v1|L5.3, C5.4, Probl2 of v1
removed|C5.2, R5.4 new, contain parts of pf of L5.3-v1|L5.2-v1 is now
L5.3,merged with concl of C5.4-v1,L5.3-v2 extends C5.4-v1|abstract, intro
updated|ref[24] added|part of L5.3-v1 is L2.1(e)-v2, another part merged with
pf of L5.2-v1 => L5.3-v
Hypomorphy of graphs up to complementation
Let be a set of cardinality (possibly infinite). Two graphs and
with vertex set are {\it isomorphic up to complementation} if is
isomorphic to or to the complement of . Let be a
non-negative integer, and are {\it -hypomorphic up to
complementation} if for every -element subset of , the induced
subgraphs and are isomorphic up to
complementation. A graph is {\it -reconstructible up to complementation}
if every graph which is -hypomorphic to up to complementation is in
fact isomorphic to up to complementation. We give a partial
characterisation of the set of pairs such that two graphs
and on the same set of vertices are equal up to complementation
whenever they are -hypomorphic up to complementation. We prove in particular
that contains all pairs such that . We
also prove that 4 is the least integer such that every graph having a
large number of vertices is -reconstructible up to complementation; this
answers a question raised by P. Ill
On Pauli Pairs
The state of a system in classical mechanics can be uniquely reconstructed if
we know the positions and the momenta of all its parts. In 1958 Pauli has
conjectured that the same holds for quantum mechanical systems. The conjecture
turned out to be wrong. In this paper we provide a new set of examples of Pauli
pairs, being the pairs of quantum states indistinguishable by measuring the
spatial location and momentum. In particular, we construct a new set of
spatially localized Pauli pairs.Comment: submitted to JM
The number of clones determined by disjunctions of unary relations
We consider finitary relations (also known as crosses) that are definable via
finite disjunctions of unary relations, i.e. subsets, taken from a fixed finite
parameter set . We prove that whenever contains at least one
non-empty relation distinct from the full carrier set, there is a countably
infinite number of polymorphism clones determined by relations that are
disjunctively definable from . Finally, we extend our result to
finitely related polymorphism clones and countably infinite sets .Comment: manuscript to be published in Theory of Computing System
Integration ontology for distributed database
In this work we will study the problem of the design of the "Integration Model for Distributed Database System". We particularly design the canonical model through the ontological handling of the information. The ontology is designed in a way that allows the description of a database like a set of representative terms of its different components. In this ontology, the definitions use classes, relations, functions, among other things, of databases, to describe their components, operations and restrictions, as well as, the process of integration. These databases can be Relational, Fuzzy, Intelligent and Multimedia1st International Workshop on Advanced Software Engineering: Expanding the Frontiers of Software Technology - Session 2: Software ModelingRed de Universidades con Carreras en Informática (RedUNCI
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