On the Intersecting Family Process
We study the intersecting family process initially studied in [Electron. J. Comb., 10:#R29 (2003)]. Here $k=k(n)$ and $E_1,E_2,\ldots,E_m$ is a random sequence of $k$-sets from $\binom{[n]}{k}$ where $E_{r+1}$ is uniformly chosen from those $k$-sets that are not already chosen and that meet $E_i,i=1,2,\ldots,r$. We prove some new results for the case where $k=cn^{1/3}$ and for the case where $k\gg n^{1/2}$.
Authors
- Patrick Bennett (ORCID: https://orcid.org/0000-0003-3147-4690)
- Wesley Pegden (ORCID: https://orcid.org/0000-0002-3680-1817)
- Alan Frieze (ORCID: https://orcid.org/0000-0002-8481-5615)
- Andrew Newman (ORCID: https://orcid.org/0000-0001-8589-459X)
Institutions
- Western Michigan University (US)
- Carnegie Mellon University (US)
Publication Details
- Journal
- The Electronic Journal of Combinatorics
- Published
- 2024-10-18
- DOI
- https://doi.org/10.37236/12060
- Primary Topic
- Family Business Performance and Succession
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Science Foundation