• 대한수학회보
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• 제49권2호
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• pp.373-379
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• 2012

In this paper, we nd the inclusion relation among four categories of posets, i.e., ideal-homogeneous, tower-homogeneous, quasi-complement-preserved, and complement-preserved posets.

• 대한수학회논문집
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• 제20권1호
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• pp.15-21
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• 2005

Null designs on the poset of dual polar spaces are considered. A poset of dual polar spaces is the set of isotropic subspaces of a finite vector space equipped with a nondegenerate bilinear form, ordered by inclusion. We show that the minimum number of isotropic subspaces to construct a nonzero null t-design is ${\prod}^{t}_{i=0}(1+q^{i})$ for the types $B_N,\;D_N$, whereas for the case of type $C_N$, more isotropic subspaces are needed.

• Kyungpook Mathematical Journal
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• 제54권2호
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• pp.197-201
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• 2014

In this paper, we study some properties of finite or infinite poset P determined by properties of the ideal based zero-divisor graph properties $G_J(P)$, for an ideal J of P.

• 호남수학학술지
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• 제40권1호
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• pp.75-82
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• 2018

Let P be a commutator poset with Z(P) its set of zero-divisors. The annihilator graph of P, denoted by AG(P), is the (undirected) graph with all elements of $Z(P){\setminus}\{0\}$ as vertices, and distinct vertices x, y are adjacent if and only if $ann(xy)\;{\neq}\;(x)\;{\cup}\;ann(y)$. In this paper, we study basic properties of AG(P).

• Kyungpook Mathematical Journal
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• 제57권3호
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• pp.385-391
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• 2017

In this paper, we study the notion of $z^J$ - ideals of posets and explore the various properties of $z^J$-ideals in posets. The relations between topological space on Sspec(P), the set $I_Q=\{x{\in}P:L(x,y){\subseteq}I\text{ for some }y{\in}P{\backslash}Q\}$ for an ideal I and a strongly prime ideal Q of P and $z^J$-ideals are discussed in poset P.

• 대한수학회보
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• 제56권1호
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• pp.1-12
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• 2019

For a finite poset $P=(X,{\preceq})$ the fractional weak discrepancy of P, denoted $wd_F(P)$, is the minimum value t for which there is a function $f:X{\rightarrow}{\mathbb{R}}$ satisfying (1) $f(x)+1{\leq}f(y)$ whenever $x{\prec}y$ and (2) ${\mid}f(x)-f(y){\mid}{\leq}t$ whenever $x{\parallel}y$. In this paper, we determine the range of the fractional weak discrepancy of (M, 2)-free posets for $M{\geq}5$, which is a problem asked in [9]. More precisely, we showed that (1) the range of the fractional weak discrepancy of (M, 2)-free interval orders is $W=\{{\frac{r}{r+1}}:r{\in}{\mathbb{N}}{\cup}\{0\}\}{\cup}\{t{\in}{\mathbb{Q}}:1{\leq}t<M-3\}$ and (2) the range of the fractional weak discrepancy of (M, 2)-free non-interval orders is $\{t{\in}{\mathbb{Q}}:1{\leq}t<M-3\}$. The result is a generalization of a well-known result for semiorders and the main result for split semiorders of [9] since the family of semiorders is the family of (4, 2)-free posets.

• 대한수학회보
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• 제32권2호
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• pp.171-177
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• 1995

Let P be a finite poset and let $\mid$P$\mid$ be the number of vertices in pp. A subposet of P is a subset of P with the induced order. A chain C in P is a subposet of P which is a linear order. The length of the chain C is $\mid$C$\mid$ - 1. A linear extension of a poset P is a linear order $L = x_1, x_2, \ldots, x_n$ of the elements of P such that $x_i < x_j$ is P implies i < j. Let L(P) be the set of all linear extensions of pp. E. Szpilrajn [5] showed that L(P) is not empty.

• 대한수학회논문집
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• 제25권1호
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• pp.19-25
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• 2010

$3{\times}3{\times}3$ is the meaningful smallest product of three chains of each size 2n+1 since $1{\times}1{\times}1$ is a 1-element poset. The linear discrepancy of the product of three chains $2n{\times}2n{\times}2n$ is found as $6n^3-2n^2-1$. But the case of the product of three chains $(2n + 1){\times}(2n + 1){\times}(2n + 1)$ is not known yet. In this paper, we determine ld$(3{\times}3{\times}3)$ as a case to determine the linear discrepancy of the product of three chains of each size 2n + 1.

• 대한수학회논문집
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• 제28권1호
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• pp.79-85
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• 2013

The structure of a poset P with smallest element 0 is looked at from two view points. Firstly, with respect to the Zariski topology, it is shown that Spec(P), the set of all prime semi-ideals of P, is a compact space and Max(P), the set of all maximal semi-ideals of P, is a compact $T_1$ subspace. Various other topological properties are derived. Secondly, we study the semi-ideal-based zero-divisor graph structure of poset P, denoted by $G_I$ (P), and characterize its diameter.

• 한국지능시스템학회논문지
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• 제19권3호
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• pp.425-431
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• 2009

By using the notion of interval-valued fuzzy relations, we forms the poset (IVFR (X), $\leq$) of interval-valued fuzzy relations on a given set X. In particular, we forms the subposet (IVFE (X), $\leq$) of interval-valued fuzzy equivalence relations on a given set X and prove that the poset (IVFE(X), $\leq$) is a complete lattice with the least element and greatest element.