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Weyl Group Multiple Dirichlet SeriesType A Combinatorial Theory (AM-175)$
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Ben Brubaker, Daniel Bump, and Solomon Friedberg

Print publication date: 2011

Print ISBN-13: 9780691150659

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691150659.001.0001

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Statement E Implies Statement D

Statement E Implies Statement D

Chapter:
(p.87) Chapter Fourteen Statement E Implies Statement D
Source:
Weyl Group Multiple Dirichlet Series
Author(s):

Ben Brubaker

Daniel Bump

Solomon Friedberg

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691150659.003.0014

This chapter introduces the theorem that says Statement E implies Statement D, first by fixing a nodal signature η‎ and presenting a “cut and paste” virtual resotope. It then presents the proof, whereby α‎ ∈, CPsubscript Greek small letter eta(c₀, · · ·,csubscript d) and let σ‎ = θ‎(α‎,η‎). The chapter proceeds by extending the function GΓ‎ from the set of decorated Γ‎-accordions to the free abelian group by linearity. Also the involution on decorated accordions induces an isomorphism. The relevant equation is obtained using the principle of inclusion-exclusion.

Keywords:   resotope, Statement E, Statement D, accordion, free abelian group, involution, isomorphism, inclusion-exclusion

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