Elliptic rook and file numbers

Utilizing elliptic weights, we construct an elliptic analogue of rook numbers for Ferrers boards. Our elliptic rook numbers generalize Garsia and Remmel's q-rook numbers by two additional independent parameters a and b, and a nome p. These are shown to satisfy an elliptic extension of a factorization theorem which in the classical case was established by Goldman, Joichi and White and later was extended to the q-case by Garsia and Remmel. We obtain similar results for our elliptic analogues of Garsia and Remmel's q-file numbers for skyline boards. We also provide an elliptic extension of the j-attacking model introduced by Remmel and Wachs. Various applications of our results include elliptic analogues of (generalized) Stirling numbers of the first and second kind, Lah numbers, Abel numbers, and r-restricted versions thereof.Comment: 45 pages; 3rd version shortened (elliptic rook theory for matchings has been taken out to keep the length of this paper reasonable

What Criteria are Necessary for the Selection of a Textbook for a Specifically Designed Senior Mathematics Course

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Space Programs Summary No. 37-36

Research in systems, guidance and control, space sciences, engineering, telecommunications and propulsion for space exploration program

Energy. A continuing bibliography with indexes, issue 26, 1 April - 30 June 1980

This bibliography lists 1134 reports, articles, and other documents introduced into the NASA Scientific and Technical Information System from April 1, 1980 through June 30, 1980