• East Asian mathematical journal
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• 제35권1호
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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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• 제26권2호
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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.

• 대한전자공학회논문지
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• 제15권1호
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• pp.12-18
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• 1978

Roome6)은 주어진 상태표로부터 최눈 k-CC를 구하고 이로 부터 k-SR의 종분할인 요소분할을 구하는 알고리즘을 제시하였다. 본 논문은 단순히 비트의 비교와 처리만으로 기본분할을 구할 수 있고 계산기 프로그램에 용이한 보라 개선된 두 알고리즘을 제시하였다. 기저분할의 쌍이란 개념을 정의하였고 이것을 이용함으로서 주어진 기저분할의 집합이 기저분할의 쌍의 요소만을 갖게되어 알고리즘이 간단화 되었다.

• ETRI Journal
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• 제36권4호
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• pp.635-642
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• 2014

Three-dimensional integrated circuits (3D ICs) implement heterogeneous systems in the same platform by stacking several planar chips vertically with through-silicon via (TSV) technology. 3D ICs have some advantages, including shorter interconnect lengths, higher integration density, and improved performance. Thermal-aware design would enhance the reliability and performance of the interconnects and devices. In this paper, we propose thermal-aware floorplanning with min-cut die partitioning for 3D ICs. The proposed min-cut die partition methodology minimizes the number of connections between partitions based on the min-cut theorem and minimizes the number of TSVs by considering a complementary set from the set of connections between two partitions when assigning the partitions to dies. Also, thermal-aware floorplanning methodology ensures a more even power distribution in the dies and reduces the peak temperature of the chip. The simulation results show that the proposed methodologies reduced the number of TSVs and the peak temperature effectively while also reducing the run-time.

• 대한수학회지
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• 제48권2호
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• pp.367-382
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• 2011

We establish a necessary and sufficient condition for a heptagonal knot to be figure-8 knot. The condition is described by a set of Radon partitions formed by vertices of the heptagon. In addition we relate this result to the number of nontrivial heptagonal knots in linear embeddings of the complete graph $K_7$ into $\mathbb{R}^3$.

• Kyungpook Mathematical Journal
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• 제56권3호
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• pp.657-668
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• 2016

Given a partition ${\lambda}=({\lambda}_1,{\lambda}_2,{\ldots},{\lambda}_l)$ of a positive integer n, let Tab(${\lambda}$, k) be the set of all tabloids of shape ${\lambda}$ whose weights range over the set of all k-compositions of n and ${\mathcal{OP}}^k_{\lambda}_{rev}$ the set of all ordered partitions into k blocks of the multiset $\{1^{{\lambda}_l}2^{{\lambda}_{l-1}}{\cdots}l^{{\lambda}_1}\}$. In [2], Butler introduced an inversion-like statistic on Tab(${\lambda}$, k) to show that the rank-selected $M{\ddot{o}}bius$ invariant arising from the subgroup lattice of a finite abelian p-group of type ${\lambda}$ has nonnegative coefficients as a polynomial in p. In this paper, we introduce an inversion-like statistic on the set of ordered partitions of a multiset and construct an inversion-preserving bijection between Tab(${\lambda}$, k) and ${\mathcal{OP}}^k_{\hat{\lambda}}$. When k = 2, we also introduce a major-like statistic on Tab(${\lambda}$, 2) and study its connection to the inversion statistic due to Butler.

• 산업기술연구
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• 제28권B호
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• pp.209-214
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• 2008

Set-valued attributes appear in many applications to model complex objects occurring in the real world. One of the most important operations on set-valued attributes is the set join, because it provides a various method to express complex queries. Currently proposed set join algorithms are based on block nested loop join in which inverted files are partitioned horizontally into blocks. Evaluating these joins are expensive because they generate intermediate partial results severely and finally obtain the final results after merging partial results. In this paper, we present an efficient processing of set join algorithm. We propose a new set join algorithm that vertically partitions inverted files into blocks, where each block fits in memory, and performs block nested loop join without producing intermediate results. Our experiments show that the vertical bitmap nested set join algorithm outperforms previously proposed set join algorithms.

• Journal of the Korean Statistical Society
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• 제13권2호
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• pp.114-120
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• 1984

A parallel flats fraction for the $3^n$ design is defined as union of flats ${t}At=c_i(mod 3)}, i=1,2,\cdots, f$ and is symbolically written as At=C where A is rank r. The A matrix partitions the effects into n+1 alias sets where $u=(3^{n-r}-1)/2. For each alias set the f flats produce an ACPM from which a detection matrix is constructed. The set of all possible parallel flats fraction C can be partitioned into equivalence classes. In this paper, we develop some properties of a detection matrix and C.

• Korean Journal of Mathematics
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• 제14권1호
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• pp.71-77
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• 2006

We find the ${\epsilon}$-fuzzy equivalence relation generated by the union of two ${\epsilon}$-fuzzy equivalence relations on a set, find the ${\epsilon}$-fuzzy equivalence relation generated by a fuzzy relation on a set, and find sufficient conditions for the composition ${\mu}{\circ}{\nu}$ of two ${\epsilon}$-fuzzy equivalence relations ${\mu}$ and ${\nu}$ to be the ${\epsilon}$-fuzzy equivalence relation generated by ${\mu}{\cup}{\nu}$. Also we study fuzzy partitions of ${\epsilon}$-fuzzy equivalence relations.

• Journal of the Korean Statistical Society
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• 제9권1호
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• pp.1-12
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• 1980

A parallel flats faraction for the $3^n$ factorial experiment is symbolically written as $At = C(r\timesf)$ where $A(r\timesn)$ is of rank r. The A-matrix partitions the nonnegligible effects into $(3^{n-r}-1)/2+1$ alias sets. The $U_i$ effects in the i-th alias set are related pairwise by elements from $S_3$, the symmetric group on three symbols. For each alias set the f flats produce an $f \times u_i$ alias componet permutation matrices (ACPM) with elements from $S_3$. All the information concerning the relationships among levels of the effects is contained in the ACPM.