Ordered Structures and Partitions.
Stanley, Richard.
Ordered Structures and Partitions. - 1st ed. - 1 online resource (114 pages) - Memoirs of the American Mathematical Society ; v.1 . - Memoirs of the American Mathematical Society .
Intro -- TABLE OF CONTENTS -- CHAPTER I. (P,ωm)-PARTITIONS -- 1. Introduction -- 2. Basic definitions -- 3. Generating functions for (P,ωm)-partitions -- 4. Distributive lattices -- 5. The form of the generating functions -- 6. The theory of w-separators -- 7. Generating functions in terms of ^-separators . -- 8. The polynomials W[sub(s)] (P,ω) -- 9. The numbers α(P,ωS) and B(P,ωS) -- 10. The reciprocity theorem -- 11. An application to r-dimensional partitions -- 12. Operations on ordered sets -- 13. The order polynomial and (P ,ω)-Eulerian numbers -- CHAPTER II. NATURAL LABELINGS -- 14. A Möbius-theoretic interpretation of B(S) -- 15. Some properties of B(P -- S) -- 16. The extreme-value theorem -- 17. Numerology of W[sub(S)] (P) and U[sub(m)] (P) -- 18. Chain conditions -- 19. Properties of Ω(m) -- CHAPTER III. APPLICATIONS -- 20. Some remarks on infinite P -- 21. Plane partitions -- 22. Trees -- 23. Stacks and V-partitions -- 24. Protruded partitions -- 25. Permutations -- REFERENCES.
9780821899168
Combinatorial analysis.
Partitions (Mathematics).
Euler''s numbers.
Electronic books.
QA164 -- .S73 1972eb
510/.8 s;511/.6
Ordered Structures and Partitions. - 1st ed. - 1 online resource (114 pages) - Memoirs of the American Mathematical Society ; v.1 . - Memoirs of the American Mathematical Society .
Intro -- TABLE OF CONTENTS -- CHAPTER I. (P,ωm)-PARTITIONS -- 1. Introduction -- 2. Basic definitions -- 3. Generating functions for (P,ωm)-partitions -- 4. Distributive lattices -- 5. The form of the generating functions -- 6. The theory of w-separators -- 7. Generating functions in terms of ^-separators . -- 8. The polynomials W[sub(s)] (P,ω) -- 9. The numbers α(P,ωS) and B(P,ωS) -- 10. The reciprocity theorem -- 11. An application to r-dimensional partitions -- 12. Operations on ordered sets -- 13. The order polynomial and (P ,ω)-Eulerian numbers -- CHAPTER II. NATURAL LABELINGS -- 14. A Möbius-theoretic interpretation of B(S) -- 15. Some properties of B(P -- S) -- 16. The extreme-value theorem -- 17. Numerology of W[sub(S)] (P) and U[sub(m)] (P) -- 18. Chain conditions -- 19. Properties of Ω(m) -- CHAPTER III. APPLICATIONS -- 20. Some remarks on infinite P -- 21. Plane partitions -- 22. Trees -- 23. Stacks and V-partitions -- 24. Protruded partitions -- 25. Permutations -- REFERENCES.
9780821899168
Combinatorial analysis.
Partitions (Mathematics).
Euler''s numbers.
Electronic books.
QA164 -- .S73 1972eb
510/.8 s;511/.6