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A short proof of the q-Dixon identity

2005
*
Discrete Mathematics
*

We give

doi:10.1016/j.disc.2005.04.006
fatcat:lbj5dx63fnd3vgjbuk62z5rfry
*a*simple*proof**of*Jackson's terminating*q*-analogue*of*Dixon's*identity*. ... Hence, our polynomial argument is somehow equivalent to*the*role played by*the**q*-Pfaff-Saalschütz*identity*in*the**proof**of**the**q*-*Dixon**identity*. ... In*the*last twenty years several*short**proofs**of*Dixon's*identity*have been published [3] [4] [5] . ...##
###
Contents

2005
*
Discrete Mathematics
*

Reidys On certain morphisms

doi:10.1016/s0012-365x(05)00314-6
fatcat:6suufuqjorgfxnwx4djkqep5pu
*of*sequential dynamical systems 245 Notes V.J.W. Guo and J. Zeng*A**short**proof**of**the**q*-*Dixon**identity*259 B. Wu, L. Zhang and Z. ... Stacho Edge-disjoint spanners in Cartesian products*of*graphs 167 Y. Hong and X.-D. Zhang Sharp upper and lower bounds for largest eigenvalue*of**the*Laplacian matrices*of*trees 187*A*. ...##
###
Character Sum Identities in Analogy with Special Functions Identities

1997
*
Advances in Mathematics
*

For

doi:10.1006/aima.1997.1637
fatcat:jlcmkpcnyjcblhprwkqo36ca34
*a**short*direct*proof**of**the*finite Barnes*identity*see [HP 91] , for*a*simultaneous*proof**of**the*classical and*the*finite*identity*see [HS] , for*a*connection with*the*principal series representations ... For*a**proof**of**the**identity*via*the*representations and characters*of*GL(3, F*q*) (see [HP 82] , where you can find also some more complicated*identities*). ...##
###
Index

2004
*
Journal of symbolic computation
*

and computer analysis, 463 Publisher's Note, 1 qMultiSum-

doi:10.1016/s0747-7171(03)00152-4
fatcat:gnptdsf7grf75aoiujuxvve46a
*a*package for proving*q*-hypergeometric multiple summation*identities*, 349 RIESE,*A*., qMultiSum-*a*package for proving*q*-hypergeometric multiple ... laws*of*syzygies, 499 YU, P. and YUAN, Y.,*A*matching pursuit technique for computing*the*simplest normal forms*of*vector fields, 591 ZHANG, B-Y.,*A*new elementary algorithm for proving*q*-hypergeometric ...##
###
Author index to volume 296

2005
*
Discrete Mathematics
*

Zeng,

doi:10.1016/s0012-365x(05)00315-8
fatcat:m2gwquhb4zcw5h3uc4nmsxjc2u
*A**short**proof**of**the**q*-*Dixon**identity*(2-3) 259-261 Hong, Y. and X.-D. ... Golumbic (1) 25-41 Ku¨ndgen,*A*. and M. Spangler,*A*bound on*the*total size*of**a*cut cover (1) 121-128 Kyriakoussis,*A*. and M.G. ...##
###
349. The Polar Circle

1911
*
Mathematical Gazette
*

I should be glad to meet with

doi:10.2307/3603254
fatcat:g4falfplhbgeveaxelkcny5xui
*a**short**proof*by Pure Geometry.] W. GALLATLY. foci S, S', and axes 2p, 2q, then 4R.*Q*= SA . S'A. 2. AH. ... I should be glad to meet with*a**short**proof*by Pure Geometry.] W. GALLATLY. 350. [Vol. v. p. 396.] I think that Mr. ...##
###
Gauss's 2F1(1) cannot be generalized to 2F1(x)

1992
*
Journal of Computational and Applied Mathematics
*

*A*

*short*

*proof*

*of*Wimp's theorem that asserts that 3Fz(

*a*, b, c; d, e; 1) cannot be expressed in closed form is also given. ... Using ideas

*of*Jet Wimp and Richard McIntosh, it is proved that Gauss's explicit evaluation

*of*zFI(

*a*, 6; c; 1) cannot be generalized to zFI(

*a*, 6; c; x), for arbitrary

*a*, b, c and X. ... •I

*A*

*short*

*proof*

*of*Wimp's theorem I will now give

*a*

*short*

*proof*

*of*Wimp's theorem [7] that ,F,(

*a*, b, c; d, e; 1) cannot be expressed in closed form, in

*the*form analogous to (7). ...

##
###
Page 3391 of Mathematical Reviews Vol. , Issue 86h
[page]

1986
*
Mathematical Reviews
*

*A*

*short*algebraic

*proof*is given for

*the*

*identity*S(n) = 3n(?").

*A*beautiful combinatorial interpretation

*of*this result is given in terms

*of*paths on lozenge- shaped and chevron-shaped lattices. ...

*The*author gives bijective

*proofs*-

*of*

*the*following results: (1) an explicit formula for HS, when \ = I*, (2)

*a*factorization theorem for HS, when d contains /*, (3)

*a*generalized Cauchy

*identity*, (4)

*a*...

##
###
What can we do with a Solution?

2002
*
Electronical Notes in Theoretical Computer Science
*

If S = 0 is

doi:10.1016/s1571-0661(04)80383-9
fatcat:qzycty6fizay5dl4e3bhnaomyq
*a*system*of*n equations and unknowns over C and S(α) = 0 to what extent can we compute with*the*point α? ... In particular, can we decide whether or not*a*polynomial expressions in*the*components*of*α with integral coefficients is zero? ... Sketch*of**proof*Let α be*a*solution*of**a*nonsingular set*of*elementary equations. ...##
###
Page 10 of Mathematical Reviews Vol. 29, Issue 1
[page]

1965
*
Mathematical Reviews
*

*A*

*short*new

*proof*is given

*of*

*the*famous theorem that every positive integer can be written as

*the*sum

*of*four squares. W. H. Mills (Princeton, N.J.) Yahya,

*Q*.

*A*. M. M. ... Cohen (Knoxville, Tenn.) 52 (Spanish Carlitz, L. 53

*A*basic analog

*of*

*the*multinomial theorem. Scripta Math. 26, 317-321 (1963).

*The*

*identities*n-1 n TT G+pre) = 5 prema ar, r=0 r=0 r TH

*a*-vey? ...

##
###
A short derivation of an elegant sum involving central binomial coefficients due to László via a hypergeometric series approach

2022
*
Contributions to Mathematics
*

*The*aim

*of*this

*short*note is to establish an elegant sum involving central binomial coefficients, due to L ászló [Amer. Math. Monthly 108 (2001) 851-855], via

*a*hypergeometric series approach. ... Acknowledgement

*The*work

*of*Dongkyu Lim was partially supported by

*the*National Research Foundation (NRF)

*of*Korea through

*a*grant funded by

*the*Korean government (MSIT) NRF-2021R1C1C1010902. ... We recall that

*the*generalized hypergeometric function with p numerator and

*q*denominator parameters, in terms

*of*

*the*Pochhammer symbol, is p F

*q*

*a*1 , . . . ,

*a*p b 1 , . . . , b

*q*; x = ∞ n=0 (

*a*1 ) ...

##
###
Cayley–Dixon projection operator for multi-univariate composed polynomials

2009
*
Journal of symbolic computation
*

Under some conditions, it is shown that

doi:10.1016/j.jsc.2008.07.007
fatcat:j3j6vgvjtrdgpkg4wppl3sddam
*a**Dixon*projection operator*of**the*composed system can be expressed as*a*power*of**the*resultant*of**the*outer polynomial system multiplied by powers*of**the*leading ... In this paper,*the*behavior*of**the*Cayley-*Dixon*projection operator and*the*structure*of**Dixon*matrices are analyzed for composed polynomial systems constructed from*a*multivariate system in which each ... Acknowledgements All*the*authors were supported by NSF grants, numbers CCF-0729097, CCR-0203051 and*a*grant from*the*Computer Science Research Institute at*the*Sandia National Labs. ...##
###
Page 75 of Mathematical Reviews Vol. 48, Issue 1
[page]

1974
*
Mathematical Reviews
*

points is not

*the**identity*and is semiregular on*the*remaining points; then n=p?+p and @ is either*the*alternating or*the*symmetric group.*The**proof*is elementary. J. D.*Dixon*(Ottawa, Ont.) ...*The*object*of*this*short*note is*the**proof**of**the*following theorem: Let p be an odd prime, and @*a*p?-transitive permutation group*of*degree n; assume that*the*stabilizer in G*of*p? ...##
###
An elliptic hypergeometric beta integral transformation
[article]

2009
*
arXiv
*
pre-print

Moreover it gives

arXiv:0912.3812v1
fatcat:zwyre2y7onekhaovtujkqbikta
*a*different*proof**of*an*identity*in another article by Rains. We also give some basic hypergeometric and classical limits*of*this*identity*. ...*The*classical limit gives*identities*(some known, some new) between generalizations*of**the*Selberg integral. ...*A*recent overview*of*these results is given in [11] . In this*short*article we prove*a*multivariate elliptic hypergeometric integral*identity*. ...##
###
Page 310 of Mathematical Reviews Vol. 35, Issue 2
[page]

1968
*
Mathematical Reviews
*

*The*author gives

*a*

*short*

*proof*for

*the*commutative case

*of*

*a*theorem (Schur, Zassenhaus) on complements in finite groups. {See also #1663 below.} 1662 H. ... These facts show that 2 is related to |

*a*certain class $

*of*groups all having

*the*form

*of*

*a*com- plete wreath product

*of*an abelian p-group by

*a*locally nil- | potent (p,

*q*)-group, for some p,

*q*. ...

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