TY  - BOOK
AU  - Stanley,Richard
TI  - Ordered Structures and Partitions
T2  - Memoirs of the American Mathematical Society
SN  - 9780821899168
AV  - QA164 -- .S73 1972eb 
U1  - 510/.8 s;511/.6 
PY  - 1972///
CY  - Providence
PB  - American Mathematical Society
KW  - Combinatorial analysis
KW  - Partitions (Mathematics)
KW  - Euler''s numbers
KW  - Electronic books
N1  - 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
UR  - https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3113684
ER  -