• Bulletin of the Korean Mathematical Society
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• v.59 no.5
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• pp.1279-1287
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• 2022

A partition of n is complete if every positive integer from 1 to n can be represented by the sum of its parts. The concept of complete partitions has been extended in several ways. In this paper, we consider the number of k-relaxed r-complete partitions of n and the number of double-complete partitions of n.

• East Asian mathematical journal
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• v.35 no.1
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• pp.9-15
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• 2019

Kaavya introduce an involution on the set of partitions with crank 0 and studied the number of partitions of n which are invariant under Kaavya's involution. If a partition ${\lambda}$ with crank 0 is invariant under her involution, we say ${\lambda}$ is a self-conjugate partition with crank 0. We prove that the number of such partitions of n is equal to the number of partitions with rank 0 which are invariant under the usual partition conjugation. We also study arithmetic properties of such partitions and their q-theoretic implication.

• Korean Journal of Mathematics
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• v.28 no.4
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• pp.791-802
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• 2020

We obtain a two variable generating function for the number of triangular partitions. Using this generating function, we study arithmetic properties of a certain weighted count of triangular partitions. Finally, we introduce a rank-type function for triangular partitions, which gives a combinatorial explanation for a triangular partition congruence.

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.1017-1024
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• 2023

A celebrated result in the study of integer partitions is the identity due to Lehmer whereby the number of partitions of n with an even number of even parts minus the number of partitions of n with an odd number of even parts equals the number of partitions of n into distinct odd parts. Inspired by Lehmer's identity, we prove explicit formulas for evaluating generating functions for sequences that enumerate integer partitions of fixed width with an even/odd number of even parts. We introduce a technique for decomposing the even entries of a partition in such a way so as to evaluate, using a finite sum over q-binomial coefficients, the generating function for the sequence of partitions with an even number of even parts of fixed, odd width, and similarly for the other families of fixed-width partitions that we introduce.

• Journal of the Korea Furniture Society
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• v.20 no.6
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• pp.543-551
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• 2009

The history repeatedly shows that designers have sought their creative inspiration from fine arts. was also influenced by contemporary art such as surrealism or installment works. This thesis aims to examine the inter-relationship between contemporary art and contemporary furniture design with examples of organic modernism and minimalism furniture design. Also, will be analyzed in light of such interdisciplinary relationship, explaining the significances of in scholastic perspective. The previous research analysis of finding out examples of how fine art and design sought mutual exchanges to develop will help to examine the significance of in the context of art history. This analysis could be used as an important academic material to understand the origin and characteristics of modern design furniture. The features of surrealism and minimalism will be discussed in light of their influences on and interactive relationship with organic modernism furniture design. This provides important basic material to further analyze . Furthermore, the artistic language and plastic features of contemporary sculptors and installment artists such as Jean Arp, Richard Serra and Anish Kapoor will be examined to show how integrated and combined main features of those artists. extracted cognitive and phenomenological aspects from Serra's works that overwhelm viewers with their massive scales. Somewhat abstract yet somewhat primitive and dynamic features of Arp's works was also referred to . are made of FRP, composed of three partitions and six stools. This work was analyzed in aspect of form, composition and function. They have organic and flexible formations with free composition availability which endow free disassemble and arrangement. Also, they have cognitive features as of small elements are freely dispersed upon spaces to bestow certain presences. Based on this, this thesis could develop scholastic researches that examine the mutual and interactive relationship between contemporary art and furniture design with much more detailed discussions and examples.

• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.431-437
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• 2002

Representing a positive integer in terms of a sum of smaller numbers with certain conditions has been studied since MacMahon [5] pioneered perfect partitions. The complete partitions is in this category and studied by the second author[6]. In this paper, we study complete partitions with more specified completeness, which we call the double-complete partitions.

• East Asian mathematical journal
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• v.28 no.1
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• pp.101-107
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• 2012

For each dimension exceeds 1, determining the number of multi-dimensional partitions of a positive integer is an open question in combinatorial number theory. For n ${\leq}$ 14 and d ${\geq}$ 1 we derive a formula for the function ${\wp}_d(n)$ where ${\wp}_d(n)$ denotes the number of partitions of n arranged on a d-dimensional space. We also give an another definition of the d-dimensional partitions using the union of finite number of divisor sets of integers.

• Korean Journal of Mathematics
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• v.26 no.2
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• pp.167-174
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• 2018

By acting the dihedral group $D_k$ on the set of k-tuple multi-partitions, we introduce k-gonal partitions for all positive integers k. We give generating functions for these new partition functions and investigate their arithmetic properties.

• Journal for History of Mathematics
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• v.30 no.2
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• pp.71-86
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• 2017

When looking for solutions of Jisuguimundo with magic number 88~92 and 94~98, alternating method is applied to each possible partitions of each magic number. But this method does not apply in case of finding solutions of Jisuguimundo with magic number 87, 93, and 99. In this study, it is shown that solutions of Jisuguimundo with magic number 87, 93, and 99 can be found by applying alternating method to two partitions. These two partitions are derived partitions obtained by each partitions of magic number 87, 93, and 99. If every number from 1 to 30 which satisfy every unit path of Jisuguimundo can be found in all components of these two derived partitions, that arrangement is just a solution of Jisuguimundo. The method suggested in this study is more developed one than the method which is applied to just one partition.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.8 no.2
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• pp.1-5
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• 2004

A multiplicative plane partition is a two-dimensional array of positive integers larger than 1 that are nonincreasing both from left to right and top to bottom and whose multiple is a given number n. For a natural number n, let $f_2(n)$ be the number of multiplicative plane partitions of n. In this paper, we prove $f_2(n)\;{\leq}\;n^2$ and a table of them up to $10^5$ is provided.