Abstract <p>Asymptotics are found for the coefficients of generating functions with a certain accuracy. These functions can be used to calculate the cardinalities of certain types of layers in partially ordered sets, along with values of the sums of boundary functionals in estimating the number of antichains in such posets. Some applications of the results are considered with examples.</p>

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Asymptotics of the Coefficients of Some Generating Functions

  • T. V. Andreeva,
  • Y. Liu

摘要

Abstract

Asymptotics are found for the coefficients of generating functions with a certain accuracy. These functions can be used to calculate the cardinalities of certain types of layers in partially ordered sets, along with values of the sums of boundary functionals in estimating the number of antichains in such posets. Some applications of the results are considered with examples.