12,628,895 research outputs found
Cuntz-Krieger algebras associated with Hilbert -quad modules of commuting matrices
Let be the -algebra associated with
the Hilbert -quad module arising from commuting matrices with
entries in . We will show that if the associated tiling space
is transitive, the -algebra is simple and purely infinite. In particulr, for two positive
integers , the -groups of the simple purely infinite -algebra
are computed by using the Euclidean
algorithm.Comment: 19 page
On the classification of easy quantum groups
In 2009, Banica and Speicher began to study the compact quantum subgroups of
the free orthogonal quantum group containing the symmetric group S_n. They
focused on those whose intertwiner spaces are induced by some partitions. These
so-called easy quantum groups have a deep connection to combinatorics. We
continue their work on classifying these objects introducing some new examples
of easy quantum groups. In particular, we show that the six easy groups O_n,
S_n, H_n, B_n, S_n' and B_n' split into seven cases on the side of free easy
quantum groups. Also, we give a complete classification in the half-liberated
case.Comment: 39 pages; appeared in Advances in Mathematics, Vol. 245, pages
500-533, 201
The Orchard crossing number of an abstract graph
We introduce the Orchard crossing number, which is defined in a similar way
to the well-known rectilinear crossing number. We compute the Orchard crossing
number for some simple families of graphs. We also prove some properties of
this crossing number.
Moreover, we define a variant of this crossing number which is tightly
connected to the rectilinear crossing number, and compute it for some simple
families of graphs.Comment: 17 pages, 10 figures. Totally revised, new material added. Submitte
Decompositions of complete uniform hypergraphs into Hamilton Berge cycles
In 1973 Bermond, Germa, Heydemann and Sotteau conjectured that if divides
, then the complete -uniform hypergraph on vertices has a
decomposition into Hamilton Berge cycles. Here a Berge cycle consists of an
alternating sequence of distinct vertices and
distinct edges so that each contains and . So the
divisibility condition is clearly necessary. In this note, we prove that the
conjecture holds whenever and . Our argument is based on
the Kruskal-Katona theorem. The case when was already solved by Verrall,
building on results of Bermond
Expressive Messaging on Mobile Platforms
We present a design for expressive multimodal messaging on mobile platforms. Strong context, simple text messages, and crude animations combine well to produce surprisingly expressive results
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