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.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Liu, F. Hook Length Polynomials for Plane Forests of a Certain Type. Ann. Comb. 13, 315–322 (2009). https://doi.org/10.1007/s00026-009-0028-7
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DOI: https://doi.org/10.1007/s00026-009-0028-7