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High-order interaction occurs in various complex network, such as social network, bionetwork and network medicine. Comparing with that there are a lot of well-developed math tools (from graph theory) ...
In algebraic geometry, purity refers to a diverse range of phenomena in which certain invariants or categories associated to geometric objects are insensitive to the removal of closed subsets of large...
In algebraic geometry, purity refers to a diverse range of phenomena in which certain invariants or categories associated to geometric objects are insensitive to the removal of closed subsets of large...
Turán-type problem may be one of central problems in extremal graph theory. Particularly, the Turán number of a cycle attracts much attention. In this talk, we introduce a terminology, that is, theta ...
In this talk, we give an example to illustrate how to use the hypergraph regularity lemmas. The absorbing method due to R?dl, Schacht and Szemerédi is a powerful tool in proving hypergraph Hamilton cy...
In this talk, we first introduce the definitions of equitable partitions and state the hypergraph regularity lemma due to R?dl and Schacht. Then, we give the conception of reduced hypergraphs and its ...
Hypergraph regularity lemmas are generalizations of Szemerédi's regularity lemma for graphs, which has been proved to be a powerful tool with many subsequent. In this talk, we first give a brief intro...
A cut of a hypergraph is a partition of its vertex set into two parts, and the size of the cut is the number of edges which have nonempty intersection with each of the two parts. A classical result of...
Cayley graphs form an important class of vertex-transitive graphs, which have been the object of study for many decades. These graphs admit a group of automorphisms that acts regularly (sharply-transi...
Matchings are fundamental objects in the study of graph theory. Unlike in graphs, finding maximum matchings in general hypergraphs is NP-hard -- its decision problem is actually one of the Karp’s 21 N...
The proper orientation number \Vec{\chi}(G) of a graph G is the minimum k such that there exists an orientation of the edges of G with all vertex-outdegrees at most k and such that for any adjacent ve...
The study of the 4-cycle has an important enlightening effect on the development of Turan type problems, especially the degenerate cases. In this talk, we focus on two conjectures about 4-cycles: a co...
In practice, fractional factorial split-plot (FFSP) designs are widely used when the levels of some factors are very difficult to change or control. The factors of an FFSP design are divided into two ...
Let $\{a(t):t \in \mathbb{R}\}$ be a diagonalizable subgroup of $SL(d,\mathbb{R})$ for which the expanded horosphere $U$ is abelian. By the Birkhoff ergodic theorem, for any point $x \in SL(d,\mathbb{...

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