# Extensions of umbral calculus II: double delta operators, Leibniz extensions and Hattori-Stong theorems

Francis Clarke^{[1]}; John Hunton^{[2]}; Nigel Ray^{[3]}

- [1] University of Wales Swansea, Department of Mathematics, Singleton Park, Swansea SA2 8PP (Grande-Bretagne)
- [2] University of Leicester, Department of Mathematics and Computer Science, University Road, Leicester LE1 7RH (Grande-Bretagne)
- [3] University of Manchester, Department of Mathematics, Oxford Road, Manchester M13 9PL (Grande-Bretagne)

Annales de l’institut Fourier (2001)

- Volume: 51, Issue: 2, page 297-336
- ISSN: 0373-0956

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topClarke, Francis, Hunton, John, and Ray, Nigel. "Extensions of umbral calculus II: double delta operators, Leibniz extensions and Hattori-Stong theorems." Annales de l’institut Fourier 51.2 (2001): 297-336. <http://eudml.org/doc/115917>.

@article{Clarke2001,

abstract = {We continue our programme of extending the Roman-Rota umbral calculus to the setting of
delta operators over a graded ring $E_\{*\}$ with a view to applications in algebraic
topology and the theory of formal group laws. We concentrate on the situation where
$E_\{*\}$ is free of additive torsion, in which context the central issues are number-
theoretic questions of divisibility. We study polynomial algebras which admit the action
of two delta operators linked by an invertible power series, and make related
constructions motivated by the Hattori-Stong theorem of algebraic topology. Our treatment
is couched purely in terms of the umbral calculus, but inspires novel topological
applications. In particular we obtain a generalised form of the Hattori-Stong theorem.},

affiliation = {University of Wales Swansea, Department of Mathematics, Singleton Park, Swansea SA2 8PP (Grande-Bretagne); University of Leicester, Department of Mathematics and Computer Science, University Road, Leicester LE1 7RH (Grande-Bretagne); University of Manchester, Department of Mathematics, Oxford Road, Manchester M13 9PL (Grande-Bretagne)},

author = {Clarke, Francis, Hunton, John, Ray, Nigel},

journal = {Annales de l’institut Fourier},

keywords = {umbral calculus; Hattori-Stong theorems; polynomial algebras; delta operators; power series; algebraic topology},

language = {eng},

number = {2},

pages = {297-336},

publisher = {Association des Annales de l'Institut Fourier},

title = {Extensions of umbral calculus II: double delta operators, Leibniz extensions and Hattori-Stong theorems},

url = {http://eudml.org/doc/115917},

volume = {51},

year = {2001},

}

TY - JOUR

AU - Clarke, Francis

AU - Hunton, John

AU - Ray, Nigel

TI - Extensions of umbral calculus II: double delta operators, Leibniz extensions and Hattori-Stong theorems

JO - Annales de l’institut Fourier

PY - 2001

PB - Association des Annales de l'Institut Fourier

VL - 51

IS - 2

SP - 297

EP - 336

AB - We continue our programme of extending the Roman-Rota umbral calculus to the setting of
delta operators over a graded ring $E_{*}$ with a view to applications in algebraic
topology and the theory of formal group laws. We concentrate on the situation where
$E_{*}$ is free of additive torsion, in which context the central issues are number-
theoretic questions of divisibility. We study polynomial algebras which admit the action
of two delta operators linked by an invertible power series, and make related
constructions motivated by the Hattori-Stong theorem of algebraic topology. Our treatment
is couched purely in terms of the umbral calculus, but inspires novel topological
applications. In particular we obtain a generalised form of the Hattori-Stong theorem.

LA - eng

KW - umbral calculus; Hattori-Stong theorems; polynomial algebras; delta operators; power series; algebraic topology

UR - http://eudml.org/doc/115917

ER -

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