Congruences for the Fishburn numbers

George E. Andrews; James A. Sellers

doi:10.1016/j.jnt.2014.10.001

Congruences for the Fishburn numbers

George E. Andrews, James A. Sellers

Mathematics

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

The Fishburn numbers, ξ( n), are defined by a formal power series expansion. ∑_n=0^∞ξ(n)qⁿ=1+ ∑_n=1^∞∏_j=1ⁿ(1-(1-q)^j). For half of the primes p, there is a non-empty set of numbers T( p) lying in [0, p-1] such that if j∈ T(p), then for all n≥ 0, ξ(pn+j)≡0(mod p).

Original language	English (US)
Pages (from-to)	298-310
Number of pages	13
Journal	Journal of Number Theory
Volume	161
DOIs	https://doi.org/10.1016/j.jnt.2014.10.001
State	Published - 2016

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/j.jnt.2014.10.001

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title = "Congruences for the Fishburn numbers",

abstract = "The Fishburn numbers, ξ( n), are defined by a formal power series expansion. ∑n=0∞ξ(n)qn=1+ ∑n=1∞∏j=1n(1-(1-q)j). For half of the primes p, there is a non-empty set of numbers T( p) lying in [0, p-1] such that if j∈ T(p), then for all n≥ 0, ξ(pn+j)≡0(mod p).",

author = "Andrews, {George E.} and Sellers, {James A.}",

note = "Publisher Copyright: {\textcopyright} 2014 Elsevier Inc.",

year = "2016",

doi = "10.1016/j.jnt.2014.10.001",

language = "English (US)",

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AU - Andrews, George E.

AU - Sellers, James A.

PY - 2016

Y1 - 2016

N2 - The Fishburn numbers, ξ( n), are defined by a formal power series expansion. ∑n=0∞ξ(n)qn=1+ ∑n=1∞∏j=1n(1-(1-q)j). For half of the primes p, there is a non-empty set of numbers T( p) lying in [0, p-1] such that if j∈ T(p), then for all n≥ 0, ξ(pn+j)≡0(mod p).

AB - The Fishburn numbers, ξ( n), are defined by a formal power series expansion. ∑n=0∞ξ(n)qn=1+ ∑n=1∞∏j=1n(1-(1-q)j). For half of the primes p, there is a non-empty set of numbers T( p) lying in [0, p-1] such that if j∈ T(p), then for all n≥ 0, ξ(pn+j)≡0(mod p).

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JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

Congruences for the Fishburn numbers

Abstract

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