Bijections for faces of the Shi and Catalan arrangements

DOI10.37236/10008zbMath1477.52034arXiv2008.02357OpenAlexW3217663612MaRDI QIDQ2665971

Duncan Levear

Publication date: 22 November 2021

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.02357

zbMATH Keywords

bijective proofhyperplane arrangementShi arrangementdecorated binary trees

Mathematics Subject Classification ID

Trees (05C05) Exact enumeration problems, generating functions (05A15) Combinatorial identities, bijective combinatorics (05A19) Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35)

Related Items (2)

Enumerative combinatorics. Abstracts from the workshop held December 11--17, 2022 ⋮ Activity from matroids to rooted trees and beyond

Cites Work

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• The cycle lemma and some applications
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• Orientations, semiorders, arrangements, and parking functions
• A combinatorial description of the spectrum for the Tsetlin library and its generalization to hyperplane arrangements
• Counting faces in the extended Shi arrangement
• A bijection for Shi arrangement faces
• Labeled binary trees, subarrangements of the Catalan arrangements, and Schur positivity
• Characteristic polynomials of subspace arrangements and finite fields
• The Shi arrangement and the Ish arrangement
• Bigraphical arrangements
• Topics in Hyperplane Arrangements
• GENERALIZED CATALAN NUMBERS, WEYL GROUPS AND ARRANGEMENTS OF HYPERPLANES
• Hyperplane arrangements, interval orders, and trees.
• Catalan Numbers
• A Combinatorial Reciprocity Theorem for Hyperplane Arrangements

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