Method for constructing bijections for classical partition identities
نویسندگان
چکیده
منابع مشابه
Partition Identities and Geometric Bijections
We present a geometric framework for a class of partition identities. We show that there exists a unique bijection proving these identities, which satisfies certain linearity conditions. In particular, we show that Corteel’s bijection enumerating partitions with nonnegative r-th differences can be obtained by our approach. Other examples and generalizations are presented.
متن کاملBijections for Hook Pair Identities
Short, bijective proofs of identities for multisets of ‘hook pairs’ (arm-leg pairs) of the cells of certain diagrams are given. These hook pair identities were originally found by Regev.
متن کاملBijections and Congruences for Generalizations of Partition Identities of Euler and Guy
In 1958, Richard Guy proved that the number of partitions of n into odd parts greater than one equals the number of partitions of n into distinct parts with no powers of 2 allowed, which is closely related to Euler’s famous theorem that the number of partitions of n into odd parts equals the number of partitions of n into distinct parts. We consider extensions of Guy’s result, which naturally l...
متن کاملPartition Bijections, a Survey
We present an extensive survey of bijective proofs of classical partitions identities. While most bijections are known, they are often presented in a different, sometimes unrecognizable way. Various extensions and generalizations are added in the form of exercises.
متن کاملConstructing Sequential Bijections
We state a simple condition on a rational subset X of a free monoid B for the existence of a sequential function that is a one-to-one mapping of some free monoid A onto X. As a by-product we obtain new sequential bijections of a free monoid onto another.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 1981
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.78.4.2026