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pro vyhledávání: '"In, MyungHo"'
Autor:
Choi, Myungho, Kim, Suh-Ryung
We say that a digraph $D$ is $(i,j)$-step competitive if any two vertices have an $(i,j)$-step common out-neighbor in $D$ and that a graph $G$ is $(i,j)$-step competitively orientable if there exists an $(i,j)$-step competitive orientation of $G$. In
Externí odkaz:
http://arxiv.org/abs/2410.04379
Autor:
Kashiwara, Masaki, Kim, Myungho
Admissible chains of i-boxes are important combinatorial tools in the monoidal categorification of cluster algebras, as they provide seeds of the cluster algebra. In this paper, we explore the properties of maximal commuting families of i-boxes in a
Externí odkaz:
http://arxiv.org/abs/2409.14359
We introduce a family of automorphisms on the bosonic extension of arbitrary type and show that they satisfy the braid relations. They preserve the global basis and the crystal basis. Using this braid group action, we define a subalgebra for each pos
Externí odkaz:
http://arxiv.org/abs/2408.07312
In the paper, we establish the global basis theory for the bosonic extension $\widehat{\mathcal{A}}$ associated with an arbitrary generalized Cartan matrix. When $\widehat{\mathcal{A}}$ is of simply-laced finite type, it is isomorphic to the quantum
Externí odkaz:
http://arxiv.org/abs/2406.13160
The competition-common enemy graph (CCE graph) of a digraph $D$ is the graph with the vertex set $V(D)$ and an edge $uv$ if and only if $u$ and $v$ have a common predator and a common prey in $D$. If each vertex of a digraph $D$ has indegree at most
Externí odkaz:
http://arxiv.org/abs/2405.13363
We say that a digraph is a $(t,\lambda)$-liking digraph if every $t$ vertices have exactly $\lambda$ common out-neighbors. In 1975, Plesn\'{i}k [Graphs with a homogeneity, 1975. {\it Glasnik Mathematicki} 10:9-23] proved that any $(t,1)$-liking digra
Externí odkaz:
http://arxiv.org/abs/2405.02662
Autor:
Choi, Myungho, Kim, Suh-Ryung
A multipartite tournament is an orientation of a complete $k$-partite graph for some positive integer $k\geq 3$. We say that a multipartite tournament $D$ is tight if every partite set forms a clique in the $(1,2)$-step competition graph, denoted by
Externí odkaz:
http://arxiv.org/abs/2402.01986
Autor:
Choi, Myungho, Kim, Suh-Ryung
A multipartite tournament is an orientation of a complete $k$-partite graph for some positive integer $k\geq 3$. We say that a multipartite tournament $D$ is tight if every partite set forms a clique in the $(1,2)$-step competition graph, denoted by
Externí odkaz:
http://arxiv.org/abs/2401.17817
Motivated by recent developments in the construction of Newton--Okounkov bodies and toric degenerations via cluster algebras in [GHKK18, FO20], we consider a family of Newton--Okounkov polytopes of a complex smooth projective variety $X$ related by a
Externí odkaz:
http://arxiv.org/abs/2401.00252
Autor:
Kim, Myungho, Kim, SungSoon
We find new presentations of the modified Ariki-Koike algebra (known also as Shoji's algebra) $\mathcal H_{n,r}$ over an integral domain $R$ associated with a set of parameters $q,u_1,\ldots,u_r$ in $R$. It turns out that the algebra $\mathcal H_{n,r
Externí odkaz:
http://arxiv.org/abs/2308.10387