Some Determinants Involving Incomplete Fubini Numbers

Komatsu, Takao; Ramírez, José L.

doi:10.2478/auom-2018-0038

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Applications By the Trudi's Formula2

Restricted and Associated Fubini Numbers2

Fubini Numbers1

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Cited by 20 publications

(16 citation statements)

References 21 publications

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“…Velleman and Call [57] gave a combinatorial identity for F n , similar to (29). An alternative proof is presented next.…”

Section: Fubini Numbersmentioning

confidence: 91%

See 1 more Smart Citation

Extensions of Set Partitions and Permutations

Caicedo¹,

Moll²,

Ramírez³

et al. 2019

Electron. J. Combin.

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“…Velleman and Call [57] gave a combinatorial identity for F n , similar to (29). An alternative proof is presented next.…”

Section: Fubini Numbersmentioning

confidence: 91%

“…The equations (39) and (40) admit the following combinatorial interpretation: the expression f Remark 54. Komatsu and Ramírez [29] found the exponential generating functions for the restricted/associated Fubini numbers:…”

Section: Restricted and Associated Fubini Numbersmentioning

confidence: 99%

Extensions of Set Partitions and Permutations

Caicedo¹,

Moll²,

Ramírez³

et al. 2019

Electron. J. Combin.

Self Cite

View full text Add to dashboard Cite

show abstract

“…In addition, there exists the following inversion formula (see, e.g. [17]), which is based upon the relation: n k=0 (−1) n−k α k D(n − k) = 0 (n ≥ 1) .…”

Section: Applications By the Trudi's Formulamentioning

confidence: 99%

Hypergeometric Euler numbers

Komatsu¹,

Zhu²

2020

AIMS Mathematics

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In this paper, we introduce the hypergeometric Euler number as an analogue of the hypergeometric Bernoulli number and the hypergeometric Cauchy number. We study several expressions and sums of products of hypergeometric Euler numbers. We also introduce complementary hypergeometric Euler numbers and give some characteristic properties. There are strong reasons why these hypergeometric numbers are important. The hypergeometric numbers have one of the advantages that yield the natural extensions of determinant expressions of the numbers, though many kinds of generalizations of the Euler numbers have been considered by many authors.

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“…In addition, there exists the following inversion formula (see, e.g. [13]), which is based upon the relation: n k=0 (−1) n−k α k R(n − k) = 0 (n ≥ 1) . Lemma 7.…”

Section: Applications By the Trudi's Formula And Inversion Expressionsmentioning

confidence: 99%

Several properties of hypergeometric Bernoulli numbers

2019

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In this paper, we give the determinant expressions of the hypergeometric Bernoulli numbers, and some relations between the hypergeometric and the classical Bernoulli numbers which include Kummer's congruences. By applying Trudi's formula, we have some different expressions and inversion relations. We also determine explicit forms of convergents of the generating function of the hypergeometric Bernoulli numbers, from which several identities for hypergeometric Bernoulli numbers are given.

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Some Determinants Involving Incomplete Fubini Numbers

Abstract: We study some properties of restricted and associated Fubini numbers. In particular, they have the natural extensions of the original Fubini numbers in the sense of determinants. We also introduce modified Bernoulli and Cauchy numbers and study characteristic properties.

Cited by 20 publications

References 21 publications

Extensions of Set Partitions and Permutations

Extensions of Set Partitions and Permutations

Hypergeometric Euler numbers

Several properties of hypergeometric Bernoulli numbers

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