• School Mathematics
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• v.7 no.2
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• pp.123-137
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• 2005

Elementary combinatorial problem may be classified into three different combinatorial models(selection, distribution, partition). The main goal of this research is to determine the effect of type of combinatorial operation and implicit combinatorial model on problem difficulty. We also classified errors in the understanding combinatorial problem into error of order, repetition, permutation with repetition, confusing the type of object and cell, partition. The analysis of variance of answers from 339 students showed the influence of the implicit combinatorial model and types of combinatorial operations. As a result of clinical interviews, we particularly noticed that some students were not able to transfer the definition of combinatorial operation when changing the problem to a different combinatorial model. Moreover, we have analysed textbooks, and we have found that the exercises in these textbooks don't have various types of problems. Therefore when organizing the teaching , it is necessary to pose various types of problems and to emphasize the transition of combinatorial problem into the different models.

• Information Systems Review
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• v.8 no.2
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• pp.103-117
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• 2006

As the interest in the combinatorial auction has increased, diverse combinatorial auction market types have been proposed. Although there have been several studies on the combinatorial auction design, the studies covered some factors or partial dimensions of combinatorial auction design. Given the potential practical value of combinatorial auctions, it is necessary to approach it with an integrated and systematic design methodology for supporting a comprehensive range of combinatorial auction models. Thus, we present a systematic framework for combinatorial auction design methodology. In particular, we classified the combinatorial auction architecture types, process types, and mechanism types. This framework characterizes the different combinatorial auction models, and lead to a useful taxonomy of the combinatorial auction design factors and taxonomy of the market types by coordination among the design factors. In addition, we illustrate an n-bilateral combinatorial auction market, derived from our design methodology, to show the viability of our study.

• Proceedings of the Korea Inteligent Information System Society Conference
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• 2005.11a
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• pp.379-390
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• 2005

In this paper, we introduce a new combinatorial auction mechanism - N-Bilateral Optimized Combinatorial Auction (N-BOCA). N-BOCA is a flexible iterative combinatorial auction model that offers optimized trading for multi-suppliers and multi-purchasers in the supply chain. We design the N-BOCA system from the perspectives of architecture, protocol, and trading strategy. Under the given N-BOCA architecture and protocol, auctioneers and bidders have diverse decision strategies for winner determination. This needs flexible modeling environments. Hence, we propose an optimization modeling agent for bid and auctioneer selection. The agent has the capability to automatic model formulation for Integer Programming modeling. Finally, we show the viability of N-BOCA through prototype and experiments. The results say both higher allocation efficiency and effectiveness compared with I-to-N general combinatorial auction mechanisms.

• Korean Journal of Mathematics
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• v.22 no.2
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• pp.325-337
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• 2014

In 1911 Schur[6] derived degree and character formulas for projective representations of the symmetric groups remarkably similar to the corresponding formulas for ordinary representations. Morris[3] derived a recurrence for evaluation of spin characters and Stembridge[8] gave a combinatorial reformulation for Morris' recurrence. In this paper we give combinatorial interpretations for the orthogonality relations of spin characters based on Stembridge's combinatorial reformulation for Morris' rule.

• East Asian mathematical journal
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• v.32 no.5
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• pp.609-619
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• 2016

Folsom [10] investigated character formulas and Chaudhary [7] expressed those formulas in terms of continued fraction identities. Andrews et al. [2] introduced and investigated combinatorial partition identities. By using and combining known formulas, we aim to present certain interrelationships among character formulas, combinatorial partition identities and continued partition identities.

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.733-746
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• 2023

Let (X, d) be a semimetric space. A permutation Φ of the set X is a combinatorial self similarity of (X, d) if there is a bijective function f : d(X × X) → d(X × X) such that d(x, y) = f(d(Φ(x), Φ(y))) for all x, y ∈ X. We describe the set of all semimetrics ρ on an arbitrary nonempty set Y for which every permutation of Y is a combinatorial self similarity of (Y, ρ).

• Journal of Intelligence and Information Systems
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• v.12 no.1
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• pp.139-161
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• 2006

In this paper, we introduce a new combinatorial auction mechanism - N-Bilateral Optimized Combinatorial Auction (N-BOCA). N-BOCA is a flexible iterative combinatorial auction model that offers optimized trading for multi-suppliers and multi-purchasers in the supply chain. We design the N-BOCA system from the perspectives of architecture, protocol, and trading strategy. Under the given N-BOCA architecture and protocol, auctioneers and bidders have diverse decision strategies f3r winner determination. This needs flexible modeling environments. Hence, we propose an optimization modeling agent for bid and auctioneer selection. The agent has the capability to automatic model formulation for Integer Programming modeling. Finally, we show the viability of N-BOCA through prototype and experiments. The results say both higher allocation efficiency and effectiveness compared with 1-to-N general combinatorial auction mechanisms.

• Communications of the Korean Mathematical Society
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• v.11 no.1
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• pp.43-55
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• 1996

Explicit formulas for bi-Hermite polynomials are found and their combinatorial model is considered. This combinatorial model is a generalization of the combinatorial model of Hermite polynomials as matching polynomials.

• The Journal of Internal Korean Medicine
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• v.37 no.2
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• pp.315-321
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• 2016

Objective: This study reports on the clinical effects of combinatorial Hyulbuchuko-tang on a deep-vein thrombosis patient.Method: The deep-vein thrombosis patient was treated using combinatorial Hyulbuchuko-tang and pharmacopuncture (water-soluble carthami flos, WCF) three times a day for 33 days. The effects of deep-vein thrombosis were measured using a 0-10 numerical rating scale (NRS) and external appearance.Result: Improvements in the NRS from 7 to 2 were observed after the combinatorial Hyulbuchuko-tang treatment.Conclusions: From these results, combinatorial Hyulbuchuko-tang may be considered to show improvement for patients with deep-vein thrombosis.

• Journal of the Korean Mathematical Society
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• v.56 no.2
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• pp.353-385
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• 2019

In this paper, we introduce the notion of combinatorial Auslander-Reiten (AR) quivers for commutation classes [${\tilde{w}}]$ of w in a finite Weyl group. This combinatorial object is the Hasse diagram of the convex partial order ${\prec}_{[{\tilde{w}}]}$ on the subset ${\Phi}(w)$ of positive roots. By analyzing properties of the combinatorial AR-quivers with labelings and reflection functors, we can apply their properties to the representation theory of KLR algebras and dual PBW-basis associated to any commutation class [${\tilde{w}}_0$] of the longest element $w_0$ of any finite type.