منابع مشابه
Bijections on m-level rook placements
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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The objective of this research is to identify the optimal pricing strategy for paid placements on search engines’ “search-results” listings. To accomplish this we develop a mathematical model incorporating a constellation of parameters that describe buyers’ online search intensity, competition among online sellers, and co-opetition between the online sellers and search engine. This model allows...
متن کاملTwo vignettes on full rook placements
Using bijections between pattern-avoiding permutations and certain full rook placements on Ferrers boards, we give short proofs of two enumerative results. The first is a simplified enumeration of the 3124, 1234avoiding permutations, obtained recently by Callan via a complicated decomposition. The second is a streamlined bijection between 1342-avoiding permutations and permutations which can be...
متن کاملm-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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The QCD dipole picture allows to build an unified theoretical description -based on BFKL dynamicsof the total and diffractive nucleon structure functions. We use a four parameter fit to describe the 1994 H1 proton structure function F2 data in the low x, moderate Q2 range. Without any additional parameter, the gluon density and the longitudinal structure functions are predicted. The diffractive...
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ژورنال
عنوان ژورنال: The Lancet
سال: 1868
ISSN: 0140-6736
DOI: 10.1016/s0140-6736(02)20082-3