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A new method for counting trees with vertex partition

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Abstract

A direct and elementary method is provided in this paper for counting trees with vertex partition instead of recursion, generating function, functional equation, Lagrange inversion, and matrix methods used before.

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References

  1. Harary F, Tutte W T. The number of plane trees with given partition. Mathematika, 11: 99–101 (1964)

    Article  MATH  MathSciNet  Google Scholar 

  2. Harary F, Prins G, Tutte W T. The number of plane trees. Akad van W Proc, 67: 319–329 (1964)

    MathSciNet  MATH  Google Scholar 

  3. Tutte W T. The number of planted plane trees with a given partition. Amer Math Monthly, 71: 272–277 (1964)

    Article  MATH  MathSciNet  Google Scholar 

  4. Liu Y P. Some functional equations in combinatorics (in Chinese). J Xinyang College (NS). 15: 1–11 (2002)

    MATH  Google Scholar 

  5. Liu Y P. Some enumerating problems of maps with vertex partition (in Chinese). Kexue Tongbao, 31: 1009–1014 (1986)

    MATH  Google Scholar 

  6. Wu F E, Liu Y P. Enumerations of one-vertex maps with face partition on the plane. Acta Math Sci Ser B, 20: 229–234 (2000)

    MATH  MathSciNet  Google Scholar 

  7. Liu Y P. Algebraic Principles of Maps (in Chinese). Beijing: Higher Education, 2007

    Google Scholar 

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Correspondence to YanPei Liu.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant No. 10571013)

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Liu, Y. A new method for counting trees with vertex partition. Sci. China Ser. A-Math. 51, 2000–2004 (2008). https://doi.org/10.1007/s11425-007-0195-0

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  • DOI: https://doi.org/10.1007/s11425-007-0195-0

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