A numeral system for the middle-levels graphs
A sequence S of restricted-growth strings unifies the presentation of middle-levels graphs Mk as follows, for 0 < k ∈ Z. Recall Mk is the subgraph in the Hasse diagram of the Boolean lattice 2[2k+1] induced by the k- and (k+1)-levels. The dihedral group D4k+2 acts on Mk via translations mod (2k +...
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| Format: | EJournal Article |
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GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB,
2021-04-15.
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| LEADER | 02070 am a22002533u 4500 | ||
|---|---|---|---|
| 001 | EJGTA_613_pdf_168 | ||
| 042 | |a dc | ||
| 100 | 1 | 0 | |a Dejter, Italo J.; University of Puerto Rico Rio Piedras, PR |d 0936-8377. |e author |
| 100 | 1 | 0 | |e contributor |
| 245 | 0 | 0 | |a A numeral system for the middle-levels graphs |
| 260 | |b GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, |c 2021-04-15. | ||
| 500 | |a https://www.ejgta.org/index.php/ejgta/article/view/613 | ||
| 520 | |a A sequence S of restricted-growth strings unifies the presentation of middle-levels graphs Mk as follows, for 0 < k ∈ Z. Recall Mk is the subgraph in the Hasse diagram of the Boolean lattice 2[2k+1] induced by the k- and (k+1)-levels. The dihedral group D4k+2 acts on Mk via translations mod (2k + 1) and complemented reversals.The first (2k)!/(k!(k+1)!) terms of S stand for the orbits of V(Mk) under such D4k+2-action, via the lexical matching colors 0, 1, ... , k on the k+1 edges at each vertex. So, S is proposed here as a convenient numeral system for the graphs Mk. Color 0 allows to reorder S via an integer sequence that behaves as an idempotent permutation on its first (2k)!/(k!(k+1)!) terms, for each 0 < k ∈ Z. Related properties hold for the remaining colors 1, ... , k. | ||
| 540 | |a Copyright (c) 2021 Electronic Journal of Graph Theory and Applications (EJGTA) | ||
| 546 | |a eng | ||
| 690 | |a numeral system, middle-levels graph, Boolean lattice, Hasse diagram, complemented reversal | ||
| 690 | |a 05C62, 05C75, 06A05, 05C69, 05C45 | ||
| 655 | 7 | |a info:eu-repo/semantics/article |2 local | |
| 655 | 7 | |a info:eu-repo/semantics/publishedVersion |2 local | |
| 655 | 7 | |a Peer-reviewed Article |2 local | |
| 786 | 0 | |n Electronic Journal of Graph Theory and Applications (EJGTA); Vol 9, No 1 (2021): Electronic Journal of Graph Theory and Applications; 137 - 156 | |
| 786 | 0 | |n 2338-2287 | |
| 787 | 0 | |n https://www.ejgta.org/index.php/ejgta/article/view/613/pdf_168 | |
| 856 | 4 | 1 | |u https://www.ejgta.org/index.php/ejgta/article/view/613/pdf_168 |z Get Fulltext |