ZEROS OF THE MOBIUS FUNCTION OF PERMUTATIONS

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10398869" target="_blank" >RIV/00216208:11320/19:10398869 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=2-jsdD4UIm" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=2-jsdD4UIm</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1112/S0025579319000251" target="_blank" >10.1112/S0025579319000251</a>

Result language
angličtina
Original language name
ZEROS OF THE MOBIUS FUNCTION OF PERMUTATIONS
Original language description
We show that if a permutation pi contains two intervals of length 2, where one interval is an ascent and the other a descent, then the Mobius function mu[1, pi] of the interval [1, pi] is zero. As a consequence, we prove that the proportion of permutations of length n with principal Mobius function equal to zero is asymptotically bounded below by (1 - 1/e^2) >= 0.3995. This is the first result determining the value of mu[1, pi] for an asymptotically positive proportion of permutations pi. We further establish other general conditions on a permutation pi that ensure mu[1, pi] = 0.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GJ16-01602Y" target="_blank" >GJ16-01602Y: Topological and geometric approaches to classes of permutations and graph properties</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)