d-Complete Posets Generalize Young Diagrams for the Jeu de Taquin Property
d-Complete Posets Generalize Young Diagrams for the Jeu de Taquin Property
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d-Complete Posets 概括了 Jeu de Taquin 财产的年轻图表
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发表时间：
2009
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通讯作者：
Robert A. Proctor
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作者：
Robert A. Proctor
jeu de taquin过程通过将其条目向西北方向移动，从倾斜的标准杨格画面产生标准杨格画面。我们将这个过程推广到偏序集：任何偏序集的某些部分编号都向上移动。一个偏序集被称为具有jeu de taquin性质，如果这个过程产生的编号不依赖于在这个过程中所做的某些选择。杨图是构成标准杨图的偏序集。这些偏序集具有jeu de taquin性质。d-完备偏序集是满足一定局部结构条件的偏序集。它们是杨氏图、移位杨氏图和有根树的相互推广。证明了所有d-完备偏序集都具有jeu de taquin性质。证明表明，每个d-完全偏序集实际上具有更强的“同时”性质，这可能导致对主要结果的代数理解。一个部分的匡威是：“非重叠”的同时偏序集是d-完全的。
The jeu de taquin process produced a standard Young tableau from a skew standard Young tableau by shifting its entries to the northwest. We generalize this process to posets: certain partial numberings of any poset are shifted upward. A poset is said to have the jeu de taquin property if the numberings resulting from this process do not depend upon certain choices made during the process. Young diagrams are the posets which underlie standard Young tableaux. These posets have the jeu de taquin property. d-Complete posets are posets which satisfy certain local structual conditions. They are mutual generalizations of Young diagrams, shifted Young diagrams, and rooted trees. We prove that all d-complete posets have the jeu de taquin property. The proof shows that each d-complete poset actually has the stronger "simultaneous" property; this may lead to an algebraic understanding of the main result. A partial converse is stated: "Non-overlapping" simultaneous posets are d-complete.