On Hankel determinants for Dyck paths with peaks avoiding multiple classes of heights

Chien, Hsu Lin; Eu, Sen Peng; Fu, Tung-Shan

doi:10.1016/j.ejc.2021.103478

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Hankel Determinants For Generating Functions Given a Generat...1

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2022

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Cited by 2 publications

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“…) and H n (D {5,{1,3,4}} ) = H 1 n (D {5,{2,4,5}} ). This agrees with direction computation or Table 1 in [1] that…”

Section: {1}supporting

confidence: 91%

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Proof of a Conjecture on Hankel Determinants for Dyck Paths with Restricted Peak Heights

Xin¹,

Zhang²

2021

Preprint

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For any integer m ≥ 2 and r ∈ {1, . . . , m}, let f m,r n denote the number of n-Dyck paths whose peak's heights are im + r for some integer i. We find the generating function of f m,r n satisfies a simple algebraic functional equation of degree 2. The r = m case is particularly nice and we give a combinatorial proof. By using the Sulanke and Xin's continued fraction method, we calculate the Hankel determinants for f m,r n . The special case r = m of our result solves a conjecture proposed by Chien, Eu and Fu. We also enriched the class of eventually periodic Hankel determinant sequences.

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“…) and H n (D {5,{1,3,4}} ) = H 1 n (D {5,{2,4,5}} ). This agrees with direction computation or Table 1 in [1] that…”

Section: {1}supporting

confidence: 91%

“…Recently in [1], Chien-Eu-Fu studied the generating function D m,V . They found plenty of cases such that the sequence of Hankel determinants H n (D {m,V } ) is periodic.…”

Section: Hankel Determinants For Generating Functions Given a Generat...mentioning

confidence: 99%

Proof of a Conjecture on Hankel Determinants for Dyck Paths with Restricted Peak Heights

Xin¹,

Zhang²

2021

Preprint

View full text Add to dashboard Cite

show abstract

Proof of a conjecture on Hankel determinants for Dyck paths with restricted peak heights

Xin

Zhang

2022

Discrete Mathematics

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On Hankel determinants for Dyck paths with peaks avoiding multiple classes of heights

Cited by 2 publications

References 13 publications

Proof of a Conjecture on Hankel Determinants for Dyck Paths with Restricted Peak Heights

Proof of a Conjecture on Hankel Determinants for Dyck Paths with Restricted Peak Heights

Proof of a conjecture on Hankel determinants for Dyck paths with restricted peak heights

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