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Hook Length Polynomials for Plane Forests of a Certain Type
Fu Liu
Department of Mathematics, University of California, Davis, One Shields Avenue, Davis, CA 95616, USA
fuliu@math.ucdavis.edu
Annals of Combinatorics 13 (3) pp.315-322 September, 2009
AMS Subject Classification: 05A15, 05A19
Abstract:
The original motivation for the study of hook length polynomials was to find a combinatorial proof for a hook length formula for binary trees given by Postnikov, as well as a proof for a hook length polynomial formula conjectured by Lascoux. In this paper, we define the hook length polynomial for plane forests of a given degree sequence type and show that it can be factored into a product of linear forms. Some other enumerative results on forests are also given.
Keywords: hook length, plane forest

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