On a combinatorial generation problem of Knuth

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10435488" target="_blank" >RIV/00216208:11320/21:10435488 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1137/1.9781611976465.46" target="_blank" >https://doi.org/10.1137/1.9781611976465.46</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/1.9781611976465.46" target="_blank" >10.1137/1.9781611976465.46</a>

Result language
angličtina
Original language name
On a combinatorial generation problem of Knuth
Original language description
The well-known middle levels conjecture asserts that for every integer n >= 1, all binary strings of length 2(n + 1) with exactly n + 1 many 0s and 1s can be ordered cyclically so that any two consecutive strings differ in swapping the first bit with a complementary bit at some later position. In his book 'The Art of Computer Programming Vol. 4A' Knuth raised a stronger form of this conjecture (Problem 56 in Section 7.2.1.3), which requires that the sequence of positions with which the first bit is swapped in each step of such an ordering has 2n + 1 blocks of the same length, and each block is obtained by adding s = 1 (modulo 2n+1) to the previous block. In this work, we prove Knuth's conjecture in a more general form, allowing for arbitrary shifts s >= 1 that are coprime to 2n + 1. We also present an algorithm to compute this ordering, generating each new bitstring in O(n) time, using O(n) memory in total.
Czech name
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Czech description
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Type
D - Article in proceedings
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
<a href="/en/project/GA19-08554S" target="_blank" >GA19-08554S: Structures and algorithms in highly symmetric graphs</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms
ISBN
978-1-61197-646-5
ISSN
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e-ISSN
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Number of pages
9
Pages from-to
735-743
Publisher name
Society for Industrial and Applied Mathematics
Place of publication
Philadelphia, USA
Event location
Alexandria, Virginia, USA (Virtual Conference)
Event date
Jan 10, 2021
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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