Ben Brubaker, Daniel Bump, and Solomon Friedberg
- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691150659
- eISBN:
- 9781400838998
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691150659.003.0014
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics
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, ...
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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.Less
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.
Ben Brubaker, Daniel Bump, and Solomon Friedberg
- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691150659
- eISBN:
- 9781400838998
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691150659.003.0013
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics
This chapter focuses on the language of resotopes and assumes that γLsubscript Greek small letter epsilon and γRsubscript Greek small letter epsilon are multiples of n for every totally resonant ...
More
This chapter focuses on the language of resotopes and assumes that γLsubscript Greek small letter epsilon and γRsubscript Greek small letter epsilon are multiples of n for every totally resonant episode. It also recalls that s and d are the weights of the accordions under consideration. It begins with the proposition that Statement D is equivalent to Statement C, and that Statement D is true if n ≠ s. It then describes the case of a totally resonant short Gelfand-Tsetlin pattern before presenting the proof that Statement D implies Statement B. It shows that the reduction to Statement D is straightforward for Class I, but each of the remaining classes involves some nuances.Less
This chapter focuses on the language of resotopes and assumes that γLsubscript Greek small letter epsilon and γRsubscript Greek small letter epsilon are multiples of n for every totally resonant episode. It also recalls that s and d are the weights of the accordions under consideration. It begins with the proposition that Statement D is equivalent to Statement C, and that Statement D is true if n ≠ s. It then describes the case of a totally resonant short Gelfand-Tsetlin pattern before presenting the proof that Statement D implies Statement B. It shows that the reduction to Statement D is straightforward for Class I, but each of the remaining classes involves some nuances.
