abstract

abstrac

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 $n$ divides $\binom{n}{k}$, then the complete $k$-uniform hypergraph on $n$ vertices has a decomposition into Hamilton Berge cycles. Here a Berge cycle consists of an alternating sequence $v_1,e_1,v_2,\dots,v_n,e_n$ of distinct vertices $v_i$ and distinct edges $e_i$ so that each $e_i$ contains $v_i$ and $v_{i+1}$. So the divisibility condition is clearly necessary. In this note, we prove that the conjecture holds whenever $k \ge 4$ and $n \ge 30$. Our argument is based on the Kruskal-Katona theorem. The case when $k=3$ 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

Tameness and Artinianness of Graded Generalized Local Cohomology Modules

Let $R=\bigoplus_{n\geq 0}R_n$, \fa\supseteq \bigoplus_{n> 0}R_n and $M$ and $N$ be a standard graded ring, an ideal of $R$ and two finitely generated graded $R$-modules, respectively. This paper studies the homogeneous components of graded generalized local cohomology modules. First of all, we show that for all $i\geq 0$, H^i_{\fa}(M, N)_n, the $n$-th graded component of the $i$-th generalized local cohomology module of $M$ and $N$ with respect to \fa, vanishes for all $n\gg 0$. Furthermore, some sufficient conditions are proposed to satisfy the equality \sup\{\en(H^i_{\fa}(M, N))| i\geq 0\}= \sup\{\en(H^i_{R_+}(M, N))| i\geq 0\}. Some sufficient conditions are also proposed for tameness of H^i_{\fa}(M, N) such that i= f_{\fa}^{R_+}(M, N) or i= \cd_{\fa}(M, N), where f_{\fa}^{R_+}(M, N) and \cd_{\fa}(M, N) denote the $R_+$-finiteness dimension and the cohomological dimension of $M$ and $N$ with respect to \fa, respectively. We finally consider the Artinian property of some submodules and quotient modules of H^j_{\fa}(M, N), where $j$ is the first or last non-minimax level of H^i_{\fa}(M, N).Comment: 18pages, with some revisions and correction

Abstract Book

Proceedings of APP 11th ANNUAL CONVENTION AND 5th INDO SWISS CONFERENCE 16 – 17, DEC-2022 &nbsp