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2004, br. 8-1, str. 15-24
Q-analog of determinant of a kind of binomial coefficient matrices
(naslov ne postoji na srpskom)
Luoyang teacher's college - Department of mathematics, Luoyang, Henan, China

Ključne reči: Gaussian binomial coefficient; matrix; determinant; Vandermonde determinant; upper triangular matrix
Sažetak
(ne postoji na srpskom)
Recently, Ratliff and Rush gave the explanation of a kind of determinant whose entries are zero and either binomial coefficients of their negative. Such work can be considered in some generalized Pascal matrices. The purpose of this paper is to establish a q-analog of the result of Ratliff and Rush. Also, a q-analogs about problem 269 in [5] are given.
 Reference Anderws, G.E. (1976) The theory of partitions. Reading, MA: Addison-Wesley Brawer, R., Pirovino, M. (1992) The linear algebra of the pascal matrix. Linear Algebra and its Applications, 174: 13 Call, G.S., Vellman, D.J. (1993) Pascal's Matrices. American Mathematical Monthly, 100(4): 372 Comtet, L. (1974) Advanced combinatorics: The art of finite and infinite expansions. Dordrecht,Boston: D. Reidel Pub. Co Fadeev, D.K., Sominskii, I.S. (1965) Problems in higher algebra. San Francisco: Freeman Johnson, W.P. (1996) q-Extensions of identities of Abel-Rothe type. Discrete Mathematics, 159 (1-3): 161 Konvalina, J. (1998) Generalized binomial coefficients and the subset-subspace problem. Advances in Applied Mathematics, 21(2): 228 Mercier, A. (1989) Identities containing Gaussian binomial coefficients. Discrete Mathematics, 76(1): 67 Mercier, A. (1990) Quelques identités pour les q-analogues. Utilitas Mathematica, 38 33-41 Moh, T.T. (1974) On the unboundedness of generators of prime ideals in power series rings of three variables, 3. Math. Soc. Jpn, 26 722-731 Ratliff, L., Rush, D.E. (1999) Triangular powers of integers from determinants of binomial coefficient matrices. Linear Algebra and its Applications, 291(1-3): 125 Roberts, P. (1994) A computation of local cohomology, in Comutative algebra: Syzygies, multiplicities, and birational algebra. Contemp. Math, 159 351-356 Singh, A.K. (1998) A computation of tight closure in diagonal hypersurfaces. Journal of Algebra, 203 (2): 579 Stanley, R.P. (1971) Theory and application of plane partitions I. Studies in Appl. Math, 50. 2 167-188 Stanley, R.P. (1971) Theory and application of plane partitions II. Studies in Appl. Math, 50. 3 51-60 Zhang, Z. (1997) The linear algebra of the generalized Pascal matrix. Linear Algebra and its Applications, 250: 51 Zhang, Z., Liu, M. (1998) An extension of the generalized pascal matrix and its algebraic properties. Linear Algebra and its Applications, 271(1-3): 169 Zhang, Z., Wang, T. (1998) Generalized Pascal matrix and recurrence sequences. Linear Algebra and its Applications, 283(1-3): 289

## O članku

DOI: 10.5937/MatMor0401015L
objavljen u SCIndeksu: 02.06.2007.

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