Geodesic
Pair analysis of involutive divisions
Fundamentalʹnaâ i prikladnaâ matematika, Tome 9 (2003) no. 3, pp. 199-212

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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 $\mathrm{Lex}$-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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     author = {A. S. Semenov},
     title = {Pair analysis of involutive divisions},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {199--212},
     publisher = {mathdoc},
     volume = {9},
     number = {3},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2003_9_3_a13/}
}
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A. S. Semenov. Pair analysis of involutive divisions. Fundamentalʹnaâ i prikladnaâ matematika, Tome 9 (2003) no. 3, pp. 199-212. http://geodesic.mathdoc.fr/item/FPM_2003_9_3_a13/