Enumerating some stable partitions involving Stirling and \(r\)-Stirling numbers of the second kind

DOI10.1007/s00009-018-1130-zzbMath1439.11071OpenAlexW2800864521MaRDI QIDQ723786

A. Medjerredine, Hacène Belbachir, Mohamed Amine Boutiche

Publication date: 24 July 2018

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00009-018-1130-z

zbMATH Keywords

generating functionsStirling numbers of the second kindchromatic polynomialset partitions\(r\)-Stirling numbers of the second kinddeletion-contraction principlegraphical Stirling numbersindependent partitionsstablesthorn graphs

Mathematics Subject Classification ID

Bell and Stirling numbers (11B73) Combinatorial identities, bijective combinatorics (05A19) Coloring of graphs and hypergraphs (05C15) Special sequences and polynomials (11B83) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items (3)

Ordinary generating function for a class of Appell polynomials and Stirling symmetric polynomials ⋮ Explicit expressions and integral representations for the Stirling numbers: a probabilistic approach ⋮ Fubini numbers and polynomials of graphs

Cites Work

• Counting the number of non-equivalent vertex colorings of a graph
• The \(r\)-Stirling numbers
• Rook theory. III: Rook polynomials and the chromatic structure of graphs
• Coloring mixed hypergraphs: theory, algorithms and applications
• Note on some restricted Stirling numbers of the second kind
• Bell numbers and \(k\)-trees
• Stirling numbers of forests and cycles
• Some applications of the chromatic polynomials
• Graph Classes: A Survey
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