In this paper,we show that there exist precisely W(A) Ferrers matrices F(C1,C2,…,cm)such that the rook polynomials is equal to the rook polynomial of Ferrers matrix F(b1,b2,…,bm), where A={b1,b2-1,…,bm-m+1} is a re...In this paper,we show that there exist precisely W(A) Ferrers matrices F(C1,C2,…,cm)such that the rook polynomials is equal to the rook polynomial of Ferrers matrix F(b1,b2,…,bm), where A={b1,b2-1,…,bm-m+1} is a repeated set,W(A) is weight of A.展开更多
Polynomial composition is the operation of replacing variables in a polynomial with other polynomials. λ-Grgbner basis is an especial Grobner basis. The main problem in the paper is: when does composition commute wi...Polynomial composition is the operation of replacing variables in a polynomial with other polynomials. λ-Grgbner basis is an especial Grobner basis. The main problem in the paper is: when does composition commute with λ-Grobner basis computation? We shall answer better the above question. This has a natural application in the computation of λ-Grobner bases.展开更多
文摘In this paper,we show that there exist precisely W(A) Ferrers matrices F(C1,C2,…,cm)such that the rook polynomials is equal to the rook polynomial of Ferrers matrix F(b1,b2,…,bm), where A={b1,b2-1,…,bm-m+1} is a repeated set,W(A) is weight of A.
基金The research is supported by the National Natural Science Foundation of China under Grant No. 10771058, Hunan Provincial Natural Science Foundation of China under Grant No. o6jj20053, and Scientific Research Fund of Hunan Provincial Education Department under Grant No. 06A017.
文摘Polynomial composition is the operation of replacing variables in a polynomial with other polynomials. λ-Grgbner basis is an especial Grobner basis. The main problem in the paper is: when does composition commute with λ-Grobner basis computation? We shall answer better the above question. This has a natural application in the computation of λ-Grobner bases.