| Title:
|
A new proof of the $q$-Dixon identity (English) |
| Author:
|
Guo, Victor J. W. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
68 |
| Issue:
|
2 |
| Year:
|
2018 |
| Pages:
|
577-580 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We give a new and elementary proof of Jackson's terminating $q$-analogue of Dixon's identity by using recurrences and induction. (English) |
| Keyword:
|
$q$-binomial coefficient |
| Keyword:
|
$q$-Dixon identity |
| Keyword:
|
recurrence |
| MSC:
|
05A30 |
| idZBL:
|
Zbl 06890391 |
| idMR:
|
MR3819192 |
| DOI:
|
10.21136/CMJ.2018.0052-17 |
| . |
| Date available:
|
2018-06-11T10:58:39Z |
| Last updated:
|
2020-07-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147237 |
| . |
| Reference:
|
[1] Andrews, G. E.: The Theory of Partitions.Cambridge University Press, Cambridge (1998). Zbl 0996.11002, MR 1634067 |
| Reference:
|
[2] Bailey, W. N.: A note on certain $q$-identities.Q. J. Math., Oxf. Ser. 12 (1941), 173-175. Zbl 0063.00168, MR 0005964, 10.1093/qmath/os-12.1.173 |
| Reference:
|
[3] Dixon, A. C.: Summation of a certain series.London M. S. Proc. 35 (1903), 284-289. Zbl 34.0490.02, MR 1576998, 10.1112/plms/s1-35.1.284 |
| Reference:
|
[4] Ekhad, S. B.: A very short proof of Dixon's theorem.J. Comb. Theory, Ser. A 54 (1990), 141-142. Zbl 0707.05007, MR 1051787, 10.1016/0097-3165(90)90014-N |
| Reference:
|
[5] Gessel, I., Stanton, D.: Short proofs of Saalschütz and Dixon's theorems.J. Comb. Theory Ser. A 38 (1985), 87-90. Zbl 0559.05008, MR 0773560, 10.1016/0097-3165(85)90026-3 |
| Reference:
|
[6] Guo, V. J. W.: A simple proof of Dixon's identity.Discrete Math. 268 (2003), 309-310. Zbl 1022.05006, MR 1983288, 10.1016/S0012-365X(03)00054-2 |
| Reference:
|
[7] Guo, V. J. W., Zeng, J.: A short proof of the q-Dixon identity.Discrete Math. 296 (2005), 259-261. Zbl 1066.05022, MR 2154718, 10.1016/j.disc.2005.04.006 |
| Reference:
|
[8] Jackson, F. H.: Certain $q$-identities.Q. J. Math., Oxford Ser. 12 (1941), 167-172. Zbl 0063.03007, MR 0005963, 0.1093/qmath/os-12.1.167 |
| Reference:
|
[9] Koepf, W.: Hypergeometric Summation---An Algorithmic Approach to Summation and Special Function Identities.Universitext, Springer, London (2014). Zbl 1296.33002, MR 3289086, 10.1007/978-1-4471-6464-7 |
| Reference:
|
[10] Mikić, J.: A proof of a famous identity concerning the convolution of the central binomial coefficients.J. Integer Seq. 19 (2016), Article ID 16.6.6, 10 pages. Zbl 1343.05015, MR 3546620 |
| Reference:
|
[11] Mikić, J.: A proof of Dixon's identity.J. Integer Seq. 19 (2016), Article ID 16.5.3, 5 pages. Zbl 06600942, MR 3514546 |
| Reference:
|
[12] Petkovšek, M., Wilf, H. S., Zeilberger, D.: A = B. With foreword by Donald E. Knuth.A. K. Peters, Wellesley (1996). Zbl 0848.05002, MR 1379802 |
| Reference:
|
[13] Zeilberger, D.: A $q$-Foata proof of the $q$-Saalschütz identity.Eur. J. Comb. 8 (1987), 461-463. Zbl 0643.05003, MR 0930183, 10.1016/S0195-6698(87)80054-9 |
| . |
