Ordered structures and partitions /
"A general theory is developed for the enumeration of order reversing maps of finite ordered sets [italic]P into chains. This theory encompasses many apparently disparate topics in combinatorial theory, including (1) ordinary partitions, (2) ordered partitions (compositions), (3) plane and mult...
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| Format: | Thesis Book |
| Language: | English |
| Published: |
Providence, R.I. :
American Mathematical Society,
[1972]
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| Series: | Memoirs of the American Mathematical Society ;
no. 119. |
| Subjects: | |
| Online Access: | Table of contents Table of contents Table of contents |
| Summary: | "A general theory is developed for the enumeration of order reversing maps of finite ordered sets [italic]P into chains. This theory encompasses many apparently disparate topics in combinatorial theory, including (1) ordinary partitions, (2) ordered partitions (compositions), (3) plane and multidimensional partitions, with applications to Young tableaux, (4) the Eulerian numbers and their refinements, (5) the tangent and secant numbers (or Euler numbers) and their refinements, (6) the indices of permutations, (7) trees, (8) stacks, and (9) protruded partitions, with applications to the Fibonacci numbers. The main tool used is that of generating functions. In particular, we study how the structure of [italic]P influences the form of the generating functions under consideration. As an application, we derive new combinatorial relationships between a finite ordered set [italic]P and its distributive lattice of order ideals."--Abstract. |
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| Physical Description: | iii, 104 pages : illustrations, diagrams ; 26 cm. |
| Bibliography: | Includes bibliographical references (pages 102-104). |
| ISBN: | 9780821818190 0821818198 |