Add to ORKGCopyright © 2013 HAN Haiqing and ZHU Siru. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Let 1 2, , , nS S SL be n finite sets of positive integers and 1 2 nS S S S = × × ×L. We have got a q q × matrix S = (gcd ( ,))i j q qd d × = , where gcd ( ,)ij i js d d =. In this paper, we study the bounds of the determinant of S, and the value of the determinant of them in special condition. Finally, we generalize the GCD matrices to the direct product of general posets and obtain some results
Let (S={1,2,..., n}) be a set of positive integers. The (ntimes n) matrix ([S]=(i,j)), where (s_{ij}...
AbstractLet e and n be positive integers and S={x1,…,xn} a set of n distinct positive integers. For ...
AbstractWe consider meet matrices on meet-semilattices as an abstract generalization of greatest com...
Copyright © 2013 HAN Haiqing and ZHU Siru. This is an open access article distributed under the Crea...
AbstractLet S = {x1, x2, …, xn} be an ordered set of distinct positive integers and [S] the GCD matr...
AbstractWe evaluate the higher-dimensional determinants of the greatest-common-divisor matrix define...
AbstractWe give a brief review of papers relating to Smith's determinant and point out a common stru...
Abstract. In this paper we defined an n × n matrix [F] = (fij) where fij = 2 2 (xi,xj) + 1, Fermat-...
AbstractLet S={x1, x2,…, xn} be a set of distinct positive integers. Then n × n matrix [S]=(Sij), wh...
Abstract. We show that with any finite partially ordered set P (which need not be a lattice) one can...
AbstractLet S={x1,…,xn} be a set of n distinct positive integers. The n×n matrix having the greatest...
Let S = {x1, x2, ..., xn} be a set of n distinct positive integers. The matrix [S] = (sij) having th...
AbstractWe consider meet matrices on posets as an abstract generalization of greatest common divisor...
Abstract. Let f be an arithmetical function. The matrix [f(i, j)]n×n given by the value of f in grea...
We have given a structure theorem for the GCD-Reciprocal LCM matrix and then we have calculated the ...
Let (S={1,2,..., n}) be a set of positive integers. The (ntimes n) matrix ([S]=(i,j)), where (s_{ij}...
AbstractLet e and n be positive integers and S={x1,…,xn} a set of n distinct positive integers. For ...
AbstractWe consider meet matrices on meet-semilattices as an abstract generalization of greatest com...
Copyright © 2013 HAN Haiqing and ZHU Siru. This is an open access article distributed under the Crea...
AbstractLet S = {x1, x2, …, xn} be an ordered set of distinct positive integers and [S] the GCD matr...
AbstractWe evaluate the higher-dimensional determinants of the greatest-common-divisor matrix define...
AbstractWe give a brief review of papers relating to Smith's determinant and point out a common stru...
Abstract. In this paper we defined an n × n matrix [F] = (fij) where fij = 2 2 (xi,xj) + 1, Fermat-...
AbstractLet S={x1, x2,…, xn} be a set of distinct positive integers. Then n × n matrix [S]=(Sij), wh...
Abstract. We show that with any finite partially ordered set P (which need not be a lattice) one can...
AbstractLet S={x1,…,xn} be a set of n distinct positive integers. The n×n matrix having the greatest...
Let S = {x1, x2, ..., xn} be a set of n distinct positive integers. The matrix [S] = (sij) having th...
AbstractWe consider meet matrices on posets as an abstract generalization of greatest common divisor...
Abstract. Let f be an arithmetical function. The matrix [f(i, j)]n×n given by the value of f in grea...
We have given a structure theorem for the GCD-Reciprocal LCM matrix and then we have calculated the ...
Let (S={1,2,..., n}) be a set of positive integers. The (ntimes n) matrix ([S]=(i,j)), where (s_{ij}...
AbstractLet e and n be positive integers and S={x1,…,xn} a set of n distinct positive integers. For ...
AbstractWe consider meet matrices on meet-semilattices as an abstract generalization of greatest com...