Bijections for 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.
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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.
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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 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 Identities
A partition of a positive integer n (or a partition of weight n) is a non-decreasing sequence λ = (λ1, λ2, . . . , λk) of non-negative integers λi such that ∑k i=1 λi = n. The λi’s are the parts of the partition λ. Integer partitions are of particular interest in combinatorics, partly because many profound questions concerning integer partitions, solved and unsolved, are easily stated, but not ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1988
ISSN: 0097-3165
DOI: 10.1016/0097-3165(88)90026-x