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RISS 인기검색어
- 검색키워드
- 저자 : Tongsuo Wu (검색결과 8 건)
- 무료
- 기관 내 무료
- 유료
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On rings whose annihilating-ideal graphs are blow-ups of a class of Boolean graphs
Jin Guo,Tongsuo Wu,Houyi Yu 대한수학회 2017 대한수학회지 Vol.54 No.3
For a finite or an infinite set $X$, let $2^X$ be the power set of $X$. A class of simple graph, called strong Boolean graph, is defined on the vertex set $2^X\setminus \{X,\,\eset\}$, with $M$ adjacent to $N$ if $M\cap N=\eset.$ In this paper, we characterize the annihilating-ideal graphs $\mathbb{AG}(R) $ that are blow-ups of strong Boolean graphs, complemented graphs and pre-atomic graphs respectively. In particular, for a commutative ring $R$ such that $\mathbb{AG}(R)$ has a maximum clique $S$ with $3\le |V(S)| \leq \infty$, we prove that $\mathbb{AG}(R)$ is a blow-up of a strong Boolean graph if and only if it is a complemented graph, if and only if $R$ is a reduced ring. If assume further that $R$ is decomposable, then we prove that $\mathbb{AG}(R)$ is a blow-up of a strong Boolean graph if and only if it is a blow-up of a pre-atomic graph. We also study the clique number and chromatic number of the graph $\mathbb{AG}(R)$.
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A CONSTRUCTION OF COMMUTATIVE NILPOTENT SEMIGROUPS
Liu, Qiong,Wu, Tongsuo,Ye, Meng Korean Mathematical Society 2013 대한수학회보 Vol.50 No.3
In this paper, we construct nilpotent semigroups S such that $S^n=\{0\}$, $S^{n-1}{\neq}\{0\}$ and ${\Gamma}(S)$ is a refinement of the star graph $K_{1,n-3}$ with center $c$ together with finitely many or infinitely many end vertices adjacent to $c$, for each finite positive integer $n{\geq}5$. We also give counting formulae to calculate the number of the mutually non-isomorphic nilpotent semigroups when $n=5$, 6 and in finite cases.
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ON THE (n, d)<sup>th</sup> f-IDEALS
GUO, JIN,WU, TONGSUO Korean Mathematical Society 2015 대한수학회지 Vol.52 No.4
For a field K, a square-free monomial ideal I of K[$x_1$, . . ., $x_n$] is called an f-ideal, if both its facet complex and Stanley-Reisner complex have the same f-vector. Furthermore, for an f-ideal I, if all monomials in the minimal generating set G(I) have the same degree d, then I is called an $(n, d)^{th}$ f-ideal. In this paper, we prove the existence of $(n, d)^{th}$ f-ideal for $d{\geq}2$ and $n{\geq}d+2$, and we also give some algorithms to construct $(n, d)^{th}$ f-ideals.
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A construction of commutative nilpotent semigroups
Qiong Liu,Tongsuo Wu,Meng Ye 대한수학회 2013 대한수학회보 Vol.50 No.3
In this paper, we construct nilpotent semigroups S such that Sn = {0}, Sn−1 6≠{0} and Γ(S) is a refinement of the star graph K1,n−3 with center c together with finitely many or infinitely many end vertices adjacent to c, for each finite positive integer n ≥ 5. We also give counting formulae to calculate the number of the mutually non-isomorphic nilpo- tent semigroups when n = 5, 6 and in finite cases.
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ON RINGS WHOSE ANNIHILATING-IDEAL GRAPHS ARE BLOW-UPS OF A CLASS OF BOOLEAN GRAPHS
Guo, Jin,Wu, Tongsuo,Yu, Houyi Korean Mathematical Society 2017 대한수학회지 Vol.54 No.3
For a finite or an infinite set X, let $2^X$ be the power set of X. A class of simple graph, called strong Boolean graph, is defined on the vertex set $2^X{\setminus}\{X,{\emptyset}\}$, with M adjacent to N if $M{\cap}N={\emptyset}$. In this paper, we characterize the annihilating-ideal graphs $\mathbb{AG}(R)$ that are blow-ups of strong Boolean graphs, complemented graphs and preatomic graphs respectively. In particular, for a commutative ring R such that AG(R) has a maximum clique S with $3{\leq}{\mid}V(S){\mid}{\leq}{\infty}$, we prove that $\mathbb{AG}(R)$ is a blow-up of a strong Boolean graph if and only if it is a complemented graph, if and only if R is a reduced ring. If assume further that R is decomposable, then we prove that $\mathbb{AG}(R)$ is a blow-up of a strong Boolean graph if and only if it is a blow-up of a pre-atomic graph. We also study the clique number and chromatic number of the graph $\mathbb{AG}(R)$.
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Jin Guo,Tongsuo Wu 대한수학회 2015 대한수학회지 Vol.52 No.4
For a field K, a square-free monomial ideal I of K[x1, . . . , xn] is called an f-ideal, if both its facet complex and Stanley-Reisner complex have the same f-vector. Furthermore, for an f-ideal I, if all monomials in the minimal generating set G(I) have the same degree d, then I is called an (n, d)th f-ideal. In this paper, we prove the existence of (n, d)th f-ideal for d ≥ 2 and n ≥ d + 2, and we also give some algorithms to construct (n, d)th f-ideals.
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STRONG SHELLABILITY OF SIMPLICIAL COMPLEXES
Guo, Jin,Shen, Yi-Huang,Wu, Tongsuo Korean Mathematical Society 2019 대한수학회지 Vol.56 No.6
Imposing a strong condition on the linear order of shellable complexes, we introduce strong shellability. Basic properties, including the existence of dimension-decreasing strong shelling orders, are developed with respect to nonpure strongly shellable complexes. Meanwhile, pure strongly shellable complexes can be characterized by the corresponding codimension one graphs. In addition, we show that the facet ideals of pure strongly shellable complexes have linear quotients.
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Strong shellability of simplicial complexes
Jin Guo,Yi-Huang Shen,Tongsuo Wu 대한수학회 2019 대한수학회지 Vol.56 No.6
Imposing a strong condition on the linear order of shellable complexes, we introduce strong shellability. Basic properties, including the existence of dimension-decreasing strong shelling orders, are developed with respect to nonpure strongly shellable complexes. Meanwhile, pure strongly shellable complexes can be characterized by the corresponding codimension one graphs. In addition, we show that the facet ideals of pure strongly shellable complexes have linear quotients.
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