Geodesic
On one combinatorial lemma
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 1, pp. 244-254
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We study $n$-dimensional cubical pseudomanifolds and their cellular mappings. In particular, consider a discrete $n$-cube and all of its $(n-1)$-faces. Then, there exists either one or two or four faces of the cube each of which is mapped to one face.
Keywords: $n$-dimensional discrete cube, cellular mapping, Hamming distance. 
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Yu. A. Shashkin. On one combinatorial lemma. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 1, pp. 244-254. http://geodesic.mathdoc.fr/item/TIMM_2010_16_1_a18/

[1] Shashkin Yu. A., “Local degrees of cubical mappings”, Proc. Steklov Inst. Math., Suppl. 2, 2001, S208–S216 | MR | Zbl