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Gaussian binomial coefficient
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== References == {{Reflist}} *Exton, H. (1983), ''q-Hypergeometric Functions and Applications'', New York: Halstead Press, Chichester: Ellis Horwood, 1983, {{ISBN|0853124914}}, {{ISBN|0470274530}}, {{ISBN|978-0470274538}} * {{cite web |first1=Eugene |last1=Mukhin |url=http://mathcircle.berkeley.edu/BMC3/SymPol.pdf |title= Symmetric Polynomials and Partitions |archive-url=https://web.archive.org/web/20160304041707/http://mathcircle.berkeley.edu/BMC3/SymPol.pdf |archive-date=March 4, 2016 |url-status=dead }} (undated, 2004 or earlier). * Ratnadha Kolhatkar, [http://www.math.mcgill.ca/goren/SeminarOnCohomology/GrassmannVarieties%20.pdf Zeta function of Grassmann Varieties] (dated January 26, 2004) * {{MathWorld| urlname=q-BinomialCoefficient|title=q-Binomial Coefficient}} * {{cite journal |first1=Henry |last1=Gould |journal=[[Fibonacci Quarterly]] |year=1969 |title=The bracket function and Fontene-Ward generalized binomial coefficients with application to Fibonomial coefficients |mr=0242691 |volume=7 |pages=23β40 |doi=10.1080/00150517.1969.12431177 }} * {{cite journal |first1= G. L. |last1=Alexanderson|author1-link=Gerald L. Alexanderson |journal=[[Fibonacci Quarterly]] |year=1974 |volume=12 |title=A Fibonacci analogue of Gaussian binomial coefficients |issue=2 |mr=0354537 |pages=129β132 |doi=10.1080/00150517.1974.12430746 }} * {{cite journal |first1=George E. |last1=Andrews |author1-link=George Andrews (mathematician) |title=Applications of basic hypergeometric functions |journal=SIAM Rev. |year=1974 |volume=16 |number=4 |jstor=2028690 |mr=0352557 |doi=10.1137/1016081 |pages=441β484 }} * {{cite journal |first1=Peter B. |last1=Borwein |title=PadΓ© approximants for the q-elementary functions |journal=Construct. Approx. |year=1988 |volume=4 |number=1 |pages=391β402 |doi=10.1007/BF02075469 |mr=0956175 |s2cid=124884851 }} * {{cite journal |first1=John |last1=Konvalina |title=Generalized binomial coefficients and the subset-subspace problem |journal=Adv. Appl. Math. |year=1998 |doi=10.1006/aama.1998.0598 |volume=21 |issue=2 |pages=228β240 |mr=1634713 |doi-access=free }} * {{cite journal |first1=A. |last1=Di Bucchianico |title=Combinatorics, computer algebra and the Wilcoxon-Mann-Whitney test |journal=J. Stat. Plann. Inf. |year=1999 |doi=10.1016/S0378-3758(98)00261-4 |volume=79 |issue=2 |pages=349β364 |citeseerx=10.1.1.11.7713 }} * {{ cite journal |first1=John |last1=Konvalina |title=A unified interpretation of the Binomial Coefficients, the Stirling numbers, and the Gaussian coefficients |journal=Amer. Math. Monthly |jstor=2695583 |year=2000 |pages=901β910 |volume=107 |number=10 |mr=1806919 |doi=10.2307/2695583 }} * {{cite journal |first1=Boris A. |last1=Kupershmidt |title=q-Newton binomial: from Euler to Gauss |journal=J. Nonlinear Math. Phys. |year=2000 |volume=7 |number=2 |pages=244β262 |mr=1763640 |bibcode=2000JNMP....7..244K |arxiv = math/0004187 |doi = 10.2991/jnmp.2000.7.2.11 |s2cid=125273424 }} * {{ cite journal |first1=Henry |last1=Cohn |journal=Amer. Math. Monthly |year=2004 |title=Projective geometry over '''F'''<sub>1</sub> and the Gaussian Binomial Coefficients |volume=111 |number=6 |jstor=4145067 |mr=2076581 |pages=487β495 |url=http://www.maa.org/programs/maa-awards/writing-awards/projective-geometry-over-f1-and-the-gaussian-binomial-coefficients |doi=10.2307/4145067 }} * {{cite journal |first1=T. |last1=Kim |title=q-Extension of the Euler formula and trigonometric functions |journal=Russ. J. Math. Phys. |volume=14 |number=3 |pages=β275β278 |year=2007 |doi=10.1134/S1061920807030041 |mr=2341775 |bibcode = 2007RJMP...14..275K |s2cid=122865930 }} * {{cite journal |first1=T. |last1=Kim |title=q-Bernoulli numbers and polynomials associated with Gaussian binomial coefficients |journal = Russ. J. Math. Phys. |volume=15 |number=1 |pages=51β57 |doi=10.1134/S1061920808010068 |mr=2390694 |year=2008|bibcode = 2008RJMP...15...51K |s2cid=122966597 }} * {{cite journal |first1=Roberto B. |last1=Corcino |title= On p,q-binomial coefficients |journal=Integers |volume=8 |year=2008 |pages=#A29 |mr=2425627 }} * {{cite web |first1=Gevorg |last1=Hmayakyan |url=http://ghmath.files.wordpress.com/2010/06/mobius.pdf |title= Recursive Formula Related To The Mobius Function }} (2009). [[Category:Q-analogs]] [[Category:Factorial and binomial topics]]
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