Lecture hall tableaux

Corteel, Sylvie; Kim, Jang Soo

doi:10.1016/j.aim.2020.107266

Cited by 3 publications

(10 citation statements)

References 23 publications

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“…We note that Theorem 3.2 can also be proved using [11,Proposition 2.10]. By taking the limit n → ∞ in Theorem 3.2 we obtain the following corollary.…”

Section: Schur Expansions Jacobi-trudi Formulas and Dualitymentioning

confidence: 81%

Refined canonical stable Grothendieck polynomials and their duals

Hwang,

Jang,

Kim

et al. 2021

Preprint

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In this paper we introduce refined canonical stable Grothendieck polynomials and their duals with two infinite sequences of parameters. These polynomials unify several generalizations of Grothendieck polynomials including canonical stable Grothendieck polynomials due to Yeliussizov, refined Grothendieck polynomials due to Chan and Pflueger, and refined dual Grothendieck polynomials due to Galashin, Liu, and Grinberg. We give Jacobi-Trudi-type formulas, combinatorial models, Schur expansions, Schur positivity, and dualities of these polynomials. We also consider flagged versions of Grothendieck polynomials and their duals with skew shapes.

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“…We note that Theorem 3.2 can also be proved using [11,Proposition 2.10]. By taking the limit n → ∞ in Theorem 3.2 we obtain the following corollary.…”

Section: Schur Expansions Jacobi-trudi Formulas and Dualitymentioning

confidence: 81%

Refined canonical stable Grothendieck polynomials and their duals

Hwang,

Jang,

Kim

et al. 2021

Preprint

Self Cite

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“…whose edge set E consists of • (nearly) horizontal edges from (i, k + r i+1 ) to (i + 1, k + r i+2 ) for i, k ∈ N and 0 ≤ r ≤ i, and • vertical edges from (i, k + r+1 i+1 ) to (i, k + r i+1 ) for i, k ∈ N and 0 ≤ r ≤ i. See Figure 2 for an example of the lecture hall graph G. We note that in [9] a slightly different graph is used to describe lecture hall tableaux, however, both graphs can equally be used for this purpose.…”

Section: Jacobi-trudi Identitymentioning

confidence: 99%

“…Proof. As in [9] the bijection between lecture hall tableaux L and non-intersecting paths (P 1 , . .…”

Section: Jacobi-trudi Identitymentioning

confidence: 99%

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Enumeration of bounded lecture hall tableaux

Corteel,

Kim

2019

Preprint

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Recently the authors introduced lecture hall tableaux in their study of multivariate little q-Jacobi polynomials. In this paper, we enumerate bounded lecture hall tableaux. We show that their enumeration is closely related to standard and semistandard Young tableaux. We also show that the number of bounded lecture hall tableaux is the coefficient of the Schur expansion of s λ (m + y 1 , . . . , m + yn). To prove this result, we use two main tools: non-intersecting lattice paths and bijections. In particular we use ideas developed by Krattenthaler to prove bijectively the hook content formula.

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“…In [9] the second and fourth authors of this paper introduced the lecture hall graph in which paths are in natural bijection with lecture hall partitions and anti-lecture hall compositions. Lecture hall partitions with n nonnegative parts were originally defined in the enumeration of certain affine permutations coming from the affine Coxeter group Cn [4].…”

Section: Introductionmentioning

confidence: 99%

Arctic Curves Phenomena for Bounded Lecture Hall Tableaux

Corteel

Keating

Nicoletti

2021

Commun. Math. Phys.

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We establish, for every family of orthogonal polynomials in the q-Askey scheme and the Askey scheme, a combinatorial model for mixed moments and coefficients in terms of paths on the lecture hall graph. This generalizes the previous results of Corteel and Kim for the little q-Jacobi polynomials. We build these combinatorial models by bootstrapping, beginning with polynomials at the bottom and working towards Askey-Wilson polynomials which sit at the top of the q-Askey scheme. As an application of the theory, we provide the first combinatorial proof of the symmetries in the parameters of the Askey-Wilson polynomials.

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Lecture hall tableaux

Cited by 3 publications

References 23 publications

Refined canonical stable Grothendieck polynomials and their duals

Refined canonical stable Grothendieck polynomials and their duals

Enumeration of bounded lecture hall tableaux

Arctic Curves Phenomena for Bounded Lecture Hall Tableaux

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