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

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
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2014 Elsevier Inc.

Keywords

(2+2)-Free posets
Ascent sequences
Bernoulli polynomials
Congruences
Fishburn numbers
Interval orders

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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).",

keywords = "(2+2)-Free posets, Ascent sequences, Bernoulli polynomials, Congruences, Fishburn numbers, Interval orders",

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)",

volume = "161",

pages = "298--310",

journal = "Journal of Number Theory",

issn = "0022-314X",

publisher = "Academic Press Inc.",

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T1 - Congruences for the Fishburn numbers

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).

KW - (2+2)-Free posets

KW - Ascent sequences

KW - Bernoulli polynomials

KW - Congruences

KW - Fishburn numbers

KW - Interval orders

UR - http://www.scopus.com/inward/record.url?scp=84961589417&partnerID=8YFLogxK

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DO - 10.1016/j.jnt.2014.10.001

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AN - SCOPUS:84961589417

SN - 0022-314X

VL - 161

SP - 298

EP - 310

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

Congruences for the Fishburn numbers

Abstract

Bibliographical note

Keywords

Publisher link

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