Bijective proofs of parity theorems for partition statistics
Journal of integer sequences, Tome 8 (2005) no. 1.

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Summary: We give bijective proofs of parity theorems for four related statistics on partitions of finite sets. A consequence of our results is a combinatorial proof of a congruence between Stirling numbers and binomial coefficients.
Classification : 11B73, 11B39
Keywords: partition statistics, q-Stirling numbers, q-Bell numbers, Fibonacci numbers
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     author = {Shattuck, Mark},
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Shattuck, Mark. Bijective proofs of parity theorems for partition statistics. Journal of integer sequences, Tome 8 (2005) no. 1. http://geodesic.mathdoc.fr/item/JIS_2005__8_1_a1/