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Pair analysis of involutive divisions

Abstract

The main goal of this work is to describe a new approach to the study of involutive divisions using the pairwise property. The paper presents a simple and intuitive method for constructing the Janet division and reveals the deep intrinsic relationship between Janet division and Lex-ordering. A method for constructing some analogues of the Janet division for other orders is described. An example of pairwise, continuous, and nonconstructive involutive division is given.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 3, pp. 199–212, 2003.

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Semenov, A.S. Pair analysis of involutive divisions. J Math Sci 135, 3400–3408 (2006). https://doi.org/10.1007/s10958-006-0169-8

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Keywords

  • Pair Analysis
  • Intuitive Method
  • Intrinsic Relationship
  • Involutive Division
  • Janet Division