Partitions with fixed largest hook length
نویسندگان
چکیده
منابع مشابه
Symmetry distribution between hook length and part length for partitions
— It is known that the two statistics on integer partitions “hook length” and “part length” are equidistributed over the set of all partitions of n. We extend this result by proving that the bivariate joint generating function by those two statistics is symmetric. Our method is based on a generating function by a triple statistic much easier to calculate.
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A pointed partition of n is a pair (λ, v) where λ ⊢ n and v is a cell in its Ferrers diagram. We construct an involution on pointed partitions of n exchanging “hook length” and “part length”. This gives a bijective proof of a recent result of Bessenrodt and Han.
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Recently, the first author has studied hook length formulas for partitions in a systematic manner. In the present paper we show that most of those hook length formulas can be generalized and include more variables via the Littlewood decomposition, which maps each partition to its t-core and t-quotient. In the case t = 2 we obtain new formulas by combining the hook lengths and BG-ranks introduce...
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ژورنال
عنوان ژورنال: The Ramanujan Journal
سال: 2017
ISSN: 1382-4090,1572-9303
DOI: 10.1007/s11139-016-9868-z