An application of the Goulden-Jackson cluster theorem

DOI10.5802/alco.210zbMath1504.05012arXiv2011.03171OpenAlexW3105950866MaRDI QIDQ2109221

Ira M. Gessel

Publication date: 20 December 2022

Published in: Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.03171

zbMATH Keywords

Möbius functionforbidden subwordsGoulden-Jackson cluster theorem

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Permutations, words, matrices (05A05)

Uses Software

• NAIVE
• DAVID_IAN
• JODO
• BLANKS
• SYMGJ
• SPGJ
• GJseries
• GJSAW
• GJsqfree

Cites Work

• Shuffle algebras, homology, and consecutive pattern avoidance
• A class of lattices with Möbius function \(\pm 1,0\)
• Enumeration of pairs of sequences by rises, falls and levels
• A generalized Goulden-Jackson cluster method and lattice path enumeration
• Finite generation for Hochschild cohomology of Gorenstein monomial algebras
• A lifting of the Goulden-Jackson cluster method to the Malvenuto-Reutenauer algebra
• Counting occurrences for a finite set of words
• On the Homology of Associative Algebras
• An Inversion Theorem for Cluster Decompositions of Sequences with Distinguished Subsequences
• Determination of a class of Poincaré series.
• The Goulden—Jackson cluster method: extensions, applications and implementations
• [https://portal.mardi4nfdi.de/wiki/Publication:5731810 On the foundations of combinatorial theory I. Theory of M�bius Functions]
• Unnamed Item

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