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  JP Journal of Algebra, Number Theory and Applications  
 ISSN: 0972-5555
 
 
 

     JP Journal of Algebra, Number Theory and Applications
    Volume 15, Issue 2, Pages 137 - 155 (December 2009)


A p, q-ANALOGUE OF THE GENERALIZED STIRLING NUMBERS

Roberto B. Corcino (Philippines) and Charles B. Montero (Philippines)

Received August 25, 2009; Revised October 6, 2009

References:



[1] L. Carlitz, q-Bernoulli numbers and polynomials, Duke Math. J. 15 (1948), 987-1000.

[2] C. C. Chen and K. M. Koh, Principles and Techniques in Combinatorics, World Scientific Publishing Co., Inc., River Edge, New Jersey, 1992.

[3] L. Comtet, Advanced Combinatorics, D. Reidel Publishing Co., Dordrecht, The Netherlands, 1974.

[4] R. B. Corcino, Some theorems on generalized Stirling numbers, Ars Combin. 60 (2001), 273-286.

[5] R. B. Corcino, On p, q-binomial coefficients, Integers: Electronic J. Combinatorial Number Theory 8(1) (2008), #A29.

[6] R. B. Corcino and C. Barrientos, Some theorems on the q-analogue of generalized Stirling numbers and the combinatorics of 0-1 tableaux, Bulletin of the Malaysian Mathematical Sciences Society, Malaysia, submitted.

[7] R. B. Corcino, L. C. Hsu and E. L. Tan, Combinatorial and statistical applications of generalized Stirling numbers, J. Math. Res. Exposition 21(3) (2001), 337-343.

[8] R. B. Corcino, L. C. Hsu and E. L. Tan, A q-analogue of generalized Stirling numbers, Fibonacci Quart. 44(2) (2006), 154-165.

[9] H. W. Gould, The q-Stirling numbers of the first and second kinds, Duke Math. J. 28 (1961), 281-289.

[10] L. C. Hsu and P. J.-S. Shiue, A unified approach to generalized Stirling numbers, Adv. in Appl. Math. 20(3) (1998), 366-384.

[11] P. Leroux, Reduced matrices and q-log-concavity properties of q-Stirling numbers, J. Combin. Theory Ser. A 54(1) (1990), 64-84.

[12] A. de Médicis and P. Leroux, Generalized Stirling numbers, convolution formulas and p, q-analogues, Canad. J. Math. 47(3) (1995), 474-499.

[13] J. B. Remmel and M. L. Wachs, Rook theory, generalized Stirling numbers and -analogues, Electron. J. Combin. 11(1) (2004), #R84.

Keywords and phrases: Stirling numbers, p, q-exponential-type Stirling numbers, p, q-binomial coefficients, q- and p, q-Stirling numbers, Ferrers diagram A-tableau.

 


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