• Korean Journal of Mathematics
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• 제17권2호
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• pp.169-179
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• 2009

Let P be a (n, n − 1, j)-poset, which is a partially ordered set of cardinality n with n − 1 maximal elements and $j(1{\leq}j{\leq}n-1)$ minimal elements, and $P^*$ the dual poset of P. In this paper, we obtain two types of incidence codes of nonempty proper subset S of P and $P^*$, respectively, by using Bogart's method [1] (see Theorem 3.3).

• 대한수학회논문집
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• 제20권1호
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• pp.1-14
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• 2005

The aim of this paper is to study order-congruences on a S-poset A and to characterize the order-congruences by the concepts of pseudooreders on A and quasi-chains module a congruence p. Some homomorphism theorems of S-posets are given which is similar to the one of ordered semigroups. Finally, It is shown that there exists the non-trivial order-congruence on a S-poset by an example.

• 대한수학회지
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• 제52권1호
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• pp.67-80
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• 2015

For a pomonoid S, let us denote Pos-S the category of S-posets and S-poset maps. In this paper, we consider the slice category Pos-S/B for an S-poset B, and study some categorical ingredients. We first show that there is no non-trivial injective object in Pos-S/B. Then we investigate injective objects with respect to the class of regular monomorphisms in this category and show that Pos-S/B has enough regular injective objects. We also prove that regular injective objects are retracts of exponentiable objects in this category. One of the main aims of the paper is to draw attention to characterizing injectivity in the category Pos-S/B under a particular case where B has trivial action. Among other things, we also prove that the necessary condition for a map (an object) here to be regular injective is being convex and present an example to show that the converse is not true, in general.

• Kyungpook Mathematical Journal
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• 제62권4호
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• pp.657-671
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• 2022

Where S is a pomonoid, let Pos-S be the category of S-posets and S-poset maps. We start off by characterizing the pomonoids S for which all projectives in this category are either generators or free. We then study the notions of regular injectivity and weakly regularly d-injectivity in this category. This leads to homological classification results for pomonoids. Among other things, we get find relationships between regular injectivity in the slice category Pos-S/BS, for any S-poset BS, and generators and cyclic projectives in Pos-S.

• 대한수학회보
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• 제54권3호
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• pp.1081-1094
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• 2017

For a poset $P=(X,{\leq}_P)$, the linear discrepancy of P is the minimum value of maximal differences of all incomparable elements for all possible labelings. In this paper, we find a lower bound and an upper bound of the linear discrepancy of a product of two posets. In order to give a lower bound, we use the known result, $ld({\mathbf{m}}{\times}{\mathbf{n}})={\lceil}{\frac{mn}{2}}{\rceil}-2$. Next, we use Dilworth's chain decomposition to obtain an upper bound of the linear discrepancy of a product of a poset and a chain. Finally, we give an example touching this upper bound.

• 호남수학학술지
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• 제43권4호
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• pp.741-749
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• 2021

A variant of up-down posets described below and the number of their linear extensions were studied. We obtained the exponential generating functions which showed that how they are related to the Euler's up-down numbers.

• 대한수학회보
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• 제61권3호
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• pp.779-784
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• 2024

Baker proved that any strongly quasi-positive fibered knot is minimal with respect to the ribbon concordance among fibered knots in the three-sphere. By applying Rapaport's conjecture, which has been solved by Kochloukova, we can check that any strongly quasi-positive fibered knot is minimal with respect to the ribbon concordance among all knots in the three-sphere. In this short note, we give an alternative proof for the fact by utilizing the knot Floer homology.