• Journal of the Korean Mathematical Society
• /
• v.51 no.2
• /
• pp.289-309
• /
• 2014

A combinatorial description of the crystal $\mathcal{B}({\infty})$ for finite-dimensional simple Lie algebras in terms of certain Young tableaux was developed by J. Hong and H. Lee. We establish an explicit bijection between these Young tableaux and canonical bases indexed by Lusztig's parametrization, and obtain a combinatorial rule for expressing the Gindikin-Karpelevich formula as a sum over the set of Young tableaux.

• Journal of the Korean Mathematical Society
• /
• v.32 no.4
• /
• pp.713-724
• /
• 1995

In 1954 Frame, Robinson and Thrall [5] gave the hook formula for the number of standard Young tableaux of a given shape. Since then many proofs for the hook formula have been given using various methods. See [9] forprobabilistic method and see [6] or [12] for combinatorial ones. Regev [10] has given asymptotic values for these numbers and Gouyou-Beauchamps [8] gave exact formulas for the number of standard Young tableaux having n cells and at most k rows in the cases k = 4 and k = 5.

• Journal of applied mathematics & informatics
• /
• v.6 no.3
• /
• pp.901-914
• /
• 1999

In [6] Schensted constructed the Schensted algorithm giving a bijection between permutations and pairs of Young standard tableaux. After knuth generalized it to column strict tableaux in [3] various analogs of the Schensted algorithm came. In this paper we describe the bumping algorithm on the shifted rim hook tableaux which is the basic building block of the Schensted algorithm for shifted rim book tableaux.

• Communications of the Korean Mathematical Society
• /
• v.12 no.3
• /
• pp.789-796
• /
• 1997

We consider a Pfaffian and its combinatorial model. We give a bijection between Pfaffian and the generating function of weights of generalized Young tableaux by this combinatorial model, and we find an explicit formula for the Pfaffian by this bijection.

• Communications of the Korean Mathematical Society
• /
• v.12 no.3
• /
• pp.786-786
• /
• 1997

• The Pure and Applied Mathematics
• /
• v.22 no.3
• /
• pp.245-261
• /
• 2015

The notion of a parabolically semistandard tableau is a generalisation of Young tableau, which explains combinatorial aspect of various Howe dualities of type A. We prove a Jacobi-Trudi type formula for the character of parabolically semistandard tableaux of a given generalised partition shape by using non-intersecting lattice paths.

• Proceedings of the Korean Information Science Society Conference
• /
• 2006.10b
• /
• pp.346-351
• /
• 2006

시맨틱 웹에 대한 관심이 높아짐과 더불어 관련 기술인 온톨로지와 이를 이용한 추론 기술 역시 이슈가 되고 있다. RacerPro, Pellet 등 지금까지의 전형적인 추론 시스템들은 주로 Tableaux Algorithm 기반의 추론 시스템으로 Tableaux Algorithm의 특성상 대용량 ABox 추론에서 문제점을 나타낸다. 이를 해결하기 위한 연구로는 Tableaux Algorithm 기반의 Instance Store와 Disjunctive Datalog Approach를 사용한 KAON2가 있다. 이러한 추론 기술에 대해서는 많은 연구가 진행되고 있지만 각 추론 시스템들에 대한 평가는 부족하다. 현재 추론 시스템들의 벤치마킹은 대부분 Tableaux Algorithm 기반의 TBox 추론에 대한 것으로 ABox 추론 및 최근 이슈인 대용량 ABox 추론에 대한 평가는 특히 부족하다. 이에 본 논문에서는 각 추론 시스템들의 이론적 배경을 근간으로 지금까지의 전형적 추론엔진들과 최근 이슈에 따른 대용량 ABox 추론을 위한 시스템들을 이론적 비교를 통해 살펴보며, 특히 대용량 ABox 추론를 위한 시스템인 Instance Store와 KAON2를 LUBM을 사용하여 평가함으로 대용량 ABox 추론에 있어 사용자의 요구에 따른 적절한 시스템을 제시한다.

• Journal of KIISE:Software and Applications
• /
• v.36 no.2
• /
• pp.153-160
• /
• 2009

As size of ontology has been increased more and more, the descriptions in the ontologies become more complicated, Therefore finding and modifying unsatisfiable concepts is hard work in ontology construction process, Minerva is an ontology reasoner which detects unsatisfiable concepts automatically and infers subsumption relation between concepts in ontology, Most description logic based ontology reasoners (including Minerva) work using tableaux algorithm, Because tableaux algorithm is very costly, ontology reasoners need various optimization methods, In this paper, we propose optimizing methods to reduce execution time of tableaux algorithm based ontology reasoner. Proposed methods were applied to Minerva which was developed as preceding study result. In consequence the new version Minerva shows high performance.

• Journal of KIISE:Software and Applications
• /
• v.34 no.7
• /
• pp.655-666
• /
• 2007

Reasoners using typical Tableaux algorithm such as RacerPro, Pellet have a problem in Tableaux algorithm large ABox reasoning. Researches to solve these Problems are dealt with Instance Store of University of Manchester which uses Tableaux algorithm based reasoner and DBMS and KAON2 of University of Karlsruhe using Disjunctive Datalog approach. An evaluation experiment for present reasoners is the experiment of TBox reasoning in most of Tableaux algorithm based one. The most of benchmarking tests in reasoning systems haven't done with ABox reasoning based Tableaux Algorithm but done with TBox reasoning based Tableaux Algorithm. Especially, rarely reported benchmarking tests in reasoners have been issued nowadays. Therefore, this thesis evaluates systems with theory of each reasoners for large ABox reasoning that becomes issues recently with typical reasoners. The large AoBx reasoning engine will be analyzed using Instance Store and KAON2 of Manchester University for large ABox processing. At the analysing method, LUBM(Lehigh University BenchMark), benchmarking test method, and it's test system will be introduced. In conclusion, I recommend appropriate reasoner in various environment with experiment result and characteristic of algorithm used for each reasoner.

• Journal of the Korean Mathematical Society
• /
• v.51 no.2
• /
• pp.427-442
• /
• 2014

A previous work gave a combinatorial description of the crystal B(${\infty}$), in terms of certain simple Young tableaux referred to as the marginally large tableaux, for finite dimensional simple Lie algebras. Using this result, we present an explicit description of the crystal B(${\lambda}$), in terms of the marginally large tableaux, for the $G_2$ Lie algebra type. We also provide a new description of B(${\lambda}$), in terms of Nakajima monomials, that is in natural correspondence with our tableau description.