A generalization of Eulerian numbers via rook placements
نویسندگان
چکیده
منابع مشابه
m-Level rook placements
Goldman, Joichi, and White proved a beautiful theorem showing that the falling factorial generating function for the rook numbers of a Ferrers board factors over the integers. Briggs and Remmel studied an analogue of rook placements where rows are replaced by sets of m rows called levels. They proved a version of the factorization theorem in that setting, but only for certain Ferrers boards. We...
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Suppose the rows of a board are partitioned into sets of m rows called levels. An m-level rook placement is a subset of the board where no two squares are in the same column or the same level. We construct explicit bijections to prove three theorems about such placements. We start with two bijections between Ferrers boards having the same number of m-level rook placements. The first generalizes...
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ژورنال
عنوان ژورنال: Involve, a Journal of Mathematics
سال: 2017
ISSN: 1944-4184,1944-4176
DOI: 10.2140/involve.2017.10.691