• Journal of the Korean Mathematical Society
• /
• v.56 no.4
• /
• pp.947-984
• /
• 2019

We provide two shifted analogues of the tableau switching process due to Benkart, Sottile, and Stroomer; the shifted tableau switching process and the modified shifted tableau switching process. They are performed by applying a sequence of elementary transformations called switches and shares many nice properties with the tableau switching process. For instance, the maps induced from these algorithms are involutive and behave very nicely with respect to the lattice property. We also introduce shifted generalized evacuation which exactly agrees with the shifted J-operation due to Worley when applied to shifted Young tableaux of normal shape. Finally, as an application, we give combinatorial interpretations of Schur P- and Schur Q-function related identities.

• Korean Journal of Mathematics
• /
• v.21 no.3
• /
• pp.223-236
• /
• 2013

Schensted algorithm was first described in 1938 by Robinson [5], in a paper dealing with an attempt to prove the correctness of the Littlewood-Richardson rule. Schensted [9] rediscovered Schensted algorithm independently in 1961 and Viennot [12] gave a geometric interpretation for Schensted algorithm in 1977. In this paper we describe some properties of Schensted algorithm using Viennot's geometric interpretation.

• Korean Journal of Mathematics
• /
• v.24 no.3
• /
• pp.469-487
• /
• 2016

In [6] Schensted constructed the Schensted algorithm, which gives a bijection between permutations and pairs of standard tableaux of the same shape. Stanton and White [8] gave analog of the Schensted algorithm for rim hook tableaux. In this paper we give a generalization of Stanton and White's Schensted algorithm for rim hook tableaux. If k is a fixed positive integer, it shows a one-to-one correspondence between all generalized hook permutations $\mathcal{H}$ of size k and all pairs (P, Q), where P and Q are semistandard k-rim hook tableaux and k-rim hook tableaux of the same shape, respectively.

• Korean Journal of Mathematics
• /
• v.16 no.3
• /
• pp.425-437
• /
• 2008

Let P be a poset and G = G(P) be the incomparability graph of P. Stanley [7] defined the chromatic symmetric function $X_{G(P)}$ which generalizes the chromatic polynomial ${\chi}_G$ of G, and showed all coefficients are nonnegative in the e-expansion of $X_{G(P)}$ for a poset P of rank 1. In this paper, we construct a sign reversing involution on the set of special rim hook P-tableaux with some conditions. It gives a combinatorial proof for (3+1)-free conjecture of a poset P of rank 1.

• The Journal of Information Systems
• /
• v.5
• /
• pp.21-41
• /
• 1996

Linear programming has become an important tool in decision-making of modern business management. This remarkable growth can be traced to the pioneering efforts of many individuals and research organizations. The popular using of personal computers make it very easy to process those complicated linear programming models. Furthermore advanced linear programming software packages assist us to solve L.P. models without any difficult process. Even though the advanced L.P. professional packages, the needs of more detailed deterministic elements for business decisions have forced us to apply dynamic approaches for more resonable solutions. For the purpose of these problems applying to the "Mathematica" packages which is composed of mathematic tools, the simplex processes show us the flexible and dynamic decision elements included to any other professional linear programming tools. Especially we need proper dynamic variables to analyze the shadow prices step by step. And applying SAS(Statistical Analysis System) packages to the L.P. problems, it is also one of the best way to get good solution. On the way trying to the other L.P. packages which are prepared for Spreadsheets i.e., MS-Excel, Lotus-123, Quatro etc. can be applied to linear programming models. But they are not so much useful for the problems. Calculating simplex tableau is an important method to interpret L.P. format for the optimal solution. In this paper we find out that the more detailed and efficient techniques to interpret useful software of mathematica and SAS for business decision making of linear programming. So it needs to apply more dynamic technique of using of Mathematica and SAS multiple software to get more efficient deterministic factors for the sophiscated L.P. solutions.

• Korean Journal of Mathematics
• /
• v.23 no.3
• /
• pp.427-438
• /
• 2015

The Schensted algorithm first described by Robinson [5] is a remarkable combinatorial correspondence associated with the theory of symmetric functions. $Sch{\ddot{u}}tzenberger's$ jeu de taquin[10] can be used to give alternative descriptions of both P- and Q-tableaux of the Schensted algorithm as well as the ordinary and dual Knuth relations. In this paper we describe the jeu de taquin on shifted rim hook tableaux using the switching rule, which shows that the sum of the weights of the shifted rim hook tableaux of a given shape and content does not depend on the order of the content if content parts are all odd.

• Proceedings of the KIPE Conference
• /
• 1998.10a
• /
• pp.859-864
• /
• 1998

Compact and small size, reliable and failsafe operation and low cost featuring fault current limiter causing the designer to take a close look into the use of passive fault current limiter(FCL) for the protection of power semiconductor devices in power electronic systems. This paper has identified the main parameters responsible for the development of ideal passive magnetic current limiter. The effect of those parameters on the range of operation and the voltage-current characteristics of the magnetic current limiter has been studied using tableau approach. Desirable characteristics are discussed and the simulation results are presented.