A jump to the Narayana number for hereditary properties of ordered 3-uniform hypergraphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10476262" target="_blank" >RIV/00216208:11320/23:10476262 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=95pq5m9Iol" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=95pq5m9Iol</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ejc.2023.103744" target="_blank" >10.1016/j.ejc.2023.103744</a>

Result language
angličtina
Original language name
A jump to the Narayana number for hereditary properties of ordered 3-uniform hypergraphs
Original language description
For k, l >= 2 we consider ideals of edge l-colored complete k-uniform hypergraphs (n, x) with vertex sets [n] = {1, 2, ... n} for n is an element of N. An ideal is a set of such colored hypergraphs that is closed under the induced ordered sub-hypergraph relation. We obtain analogues of two results of Klazar (2010) who considered graphs, namely we prove two jumps for growth functions of such ideals of colored hypergraphs. The first jump is for any k, l >= 2 and says that the growth function is either eventually constant or at least n - k + 2. The second jump is only for k = 3 and l = 2 and says that the growth function of an ideal of edge two-colored complete 3-uniform hypergraphs grows either at most polynomially, or for n >= 23 at least as Gn where Gn is the sequence defined by G1 = G2 = 1, G3 = 2 and Gn = Gn-1 + Gn-3 for n >= 4. The lower bounds in both jumps are tight. (c) 2023 Elsevier Ltd. All rights reserved.
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
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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
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Continuities
S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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