Geodesic
The negative \(q\)-binomial
Shishuo Fu1 ; V. Reiner2 ; Dennis Stanton ; Nathaniel Thiem3
1Department of Mathematical Sciences (BK21), KAIST 291 Daehak-ro Yuseong-gu, Daejeon 305-701, Republic of Korea
2School of Mathematics, Univ. of Minnesota, Minneapolis, MN 55455
3Department of Mathematics, University of Colorado, Boulder, CO 80309
The electronic journal of combinatorics, Tome 19 (2012) no. 1
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Interpretations for the $q$-binomial coefficient evaluated at $-q$ are discussed. A $(q,t)$-version is established, including an instance of a cyclic sieving phenomenon involving unitary spaces.
DOI : 10.37236/2040
Classification : 05A10, 05A17, 05E10, 20C33
Mots-clés : q-binomial, Gaussian polynomial, (q;t)-binomial, ennola duality, unitary group, unitary space, characteristic map, invariant theory, cyclic sieving phenomenon

Shishuo Fu  1   ; V. Reiner  2   ; Dennis Stanton    ; Nathaniel Thiem  3

1 Department of Mathematical Sciences (BK21), KAIST 291 Daehak-ro Yuseong-gu, Daejeon 305-701, Republic of Korea
2 School of Mathematics, Univ. of Minnesota, Minneapolis, MN 55455
3 Department of Mathematics, University of Colorado, Boulder, CO 80309 
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     title = {The negative \(q\)-binomial},
     journal = {The electronic journal of combinatorics},
     year = {2012},
     volume = {19},
     number = {1},
     doi = {10.37236/2040},
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     url = {http://geodesic.mathdoc.fr/articles/10.37236/2040/}
}
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Shishuo Fu; V. Reiner; Dennis Stanton; Nathaniel Thiem. The negative \(q\)-binomial. The electronic journal of combinatorics, Tome 19 (2012) no. 1. doi: 10.37236/2040

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