Non-crossing Trees, Quadrangular Dissections, Ternary Trees, and Duality-Preserving Bijections

Apostolakis, Nikos

doi:10.1007/s00026-021-00531-w

Cited by 2 publications

(4 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…diagrams that have a fixed ordering. We can invert (16) by treating it as a formal power series and using the Lagrange series inversion formula.…”

Section: Discussionmentioning

confidence: 99%

“…Thus, to count the number of primitive quadrangulations we just need to find the subset of quadrangulations that are invariant under some rotation. This problem has been addressed by [15] using the method of generating functions, but we shall take a simpler approach here following [16].…”

Section: Counting Primitives For the Quartic Casementioning

confidence: 99%

“…) {(15, 610),(15,18)} and {(16, 914),(16, 110),(16, 813)} respectively. The set of Q-compatible p-angulations for these are: p = 5 : S…”

mentioning

confidence: 99%

“…For P=(16,813), with ∪ i {r i s i } to be {13, 35, 15, 713, 912, 911, 812, 17, 714} 712 = c 712 + d 713 + d 812 − X 813 For P=(16,110), with ∪ i {r i s i } to be {13, 35, 15, 17, 18, 19, 113, 1113, 111}…”

mentioning

confidence: 99%

See 3 more Smart Citations

The positive geometry for 𝜙p interactions

Raman¹

2019

J. High Energ. Phys.

View full text Add to dashboard Cite

Starting with the seminal work of Arkani-Hamed et al [1], in [2], the "Amplituhedron program" was extended to analyzing (planar) amplitudes in massless φ 4 theory. In this paper we show that the program can be further extended to include φ p (p > 4) interactions. We show that tree-level planar amplitudes in these theories can be obtained from geometry of polytopes called accordiohedron which naturally sits inside kinematic space. As in the case of quartic interactions the accordiohedron of a given dimension is not unique, and we show that a weighted sum of residues of the canonical form on these polytopes can be used to compute scattering amplitudes. We finally provide a prescription to compute the weights and demonstrate how it works in various examples.1

show abstract

“…diagrams that have a fixed ordering. We can invert (16) by treating it as a formal power series and using the Lagrange series inversion formula.…”

Section: Discussionmentioning

confidence: 99%

Section: Counting Primitives For the Quartic Casementioning

confidence: 99%

“…) {(15, 610),(15,18)} and {(16, 914),(16, 110),(16, 813)} respectively. The set of Q-compatible p-angulations for these are: p = 5 : S…”

mentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations