On the growth of the Mobius function of permutations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10403028" target="_blank" >RIV/00216208:11320/20:10403028 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=0SdOBTFjoy" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=0SdOBTFjoy</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jcta.2019.105121" target="_blank" >10.1016/j.jcta.2019.105121</a>

Result language
angličtina
Original language name
On the growth of the Mobius function of permutations
Original language description
We study the values of the Mobius function mu of intervals in the containment poset of permutations. We construct a sequence of permutations pi(n) of size 2n - 2 for which mu(1, pi(n)) is given by a polynomial in n of degree 7. This construction provides the fastest known growth of vertical bar mu(1, pi)vertical bar in terms of vertical bar pi vertical bar, improving a previous quadratic bound by Smith. Our approach is based on a formula expressing the Mobil's function of an arbitrary permutation interval [alpha, beta] in terms of the number of embeddings of the elements of the interval into beta.
Czech name
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Czech description
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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
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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