The theory of partitions. (English) Zbl 0655.10001
Encyclopedia of Mathematics and its Applications, Vol. 2. Section: Number Theory. Reading, Massachusetts, etc.: Addison-Wesley Publishing Company. Advanced Book Program (1976). Cambridge etc.: Cambridge University Press. XIV, 255 p. (1984).
For a review see Zbl 0371.10001. (A Russian translation (Nauka, Moscow) was published in 1982, see Zbl 0499.10001.)
MSC:
11-02 | Research exposition (monographs, survey articles) pertaining to number theory |
11P81 | Elementary theory of partitions |
05-02 | Research exposition (monographs, survey articles) pertaining to combinatorics |
05A17 | Combinatorial aspects of partitions of integers |
05A15 | Exact enumeration problems, generating functions |
05A19 | Combinatorial identities, bijective combinatorics |
Keywords:
partitions; generating functions; asymptotic problems; partition function; congruences; restricted partitions; permutations; compositions; Newcomb’s problem; Hardy-Ramanujan-Rademacher expansion; Rogers-Ramanujan identities; higher dimensional partitions; multipartite partitions; ordered partitionsOnline Encyclopedia of Integer Sequences:
Triangle read by rows: T(n,k) (1 <= k <= n) is the total number of right angles of size k in all partitions of n.a(n) is the sum over all partitions of n of the number of right angles that are not the largest right angle.
Triangle read by rows: T(n,k) (1 <= k <= n) is the sum of the sizes of all right angles of size k of all partitions of n.