“Lengyel's Constant”的概念、定义、习题解题方法及翻译-数学辞典

单词

Lengyel's Constant

释义

Lengyel's Constant

N.B. A detailed on-line essay by S. Finchwas the starting point for this entry.

Let denote the partition lattice of the Set . The Maximum element of is

(1)

and the Minimum element is

(2)

Let

denote the number of chains of any length in

containing both

and

. Then

satisfies theRecurrence Relation

(3)

where

is a Stirling Number of the Second Kind. Lengyel (1984) proved that the Quotient

(4)

is bounded between two constants as

, and Flajolet and Salvy (1990) improved the result of Babai and Lengyel (1992) to show that

(5)

References

Babai, L. and Lengyel, T. ``A Convergence Criterion for Recurrent Sequences with Application to the Partition Lattice.'' Analysis 12, 109-119, 1992.

Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/lngy/lngy.html

Flajolet, P. and Salvy, B. ``Hierarchal Set Partitions and Analytic Iterates of the Exponential Function.'' Unpublished manuscript, 1990.

Lengyel, T. ``On a Recurrence Involving Stirling Numbers.'' Europ. J. Comb. 5, 313-321, 1984.

Plouffe, S. ``The Lengyel Constant.''http://www.lacim.uqam.ca/piDATA/lengyel.txt.

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