{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:19Z","timestamp":1753893859702,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The poset $Y_{k, 2}$ consists of $k+2$ distinct elements\u00a0 $x_1$, $x_2$, \\dots, $x_{k}$, $y_1$, $y_2$, such that $x_1 \\le x_2 \\le \\cdots \\le x_{k} \\le y_1$, $y_2$. The poset $Y'_{k, 2}$ is the dual poset of $Y_{k, 2}$. The sum of the $k$ largest binomial coefficients of order $n$ is denoted by $\\Sigma(n,k)$. Let $\\mathrm{La}^{\\sharp}(n,\\{Y_{k, 2}, Y'_{k, 2}\\})$ be the size of the largest family $\\mathcal{F} \\subset 2^{[n]}$ that contains neither $Y_{k,2}$ nor $Y'_{k,2}$ as an induced subposet. Methuku and Tompkins proved that $\\mathrm{La}^{\\sharp}(n, \\{Y_{2,2}, Y'_{2,2}\\}) = \\Sigma(n,2)$ for $n \\ge 3$ and conjectured the generalization that if $k \\ge 2$ is an integer and $n \\ge k+1$, then $\\mathrm{La}^{\\sharp}(n, \\{Y_{k,2}, Y'_{k,2}\\}) = \\Sigma(n,k)$. On the other hand, it is known that $\\mathrm{La}^{\\sharp}(n, Y_{k,2})$ and $\\mathrm{La}^{\\sharp}(n, Y'_{k,2})$ are both strictly greater than $\\Sigma(n,k)$. In this paper, we introduce a simple approach, motivated by discharging, to prove this conjecture. \u00a0<\/jats:p>","DOI":"10.37236\/7680","type":"journal-article","created":{"date-parts":[[2020,1,24]],"date-time":"2020-01-24T09:18:48Z","timestamp":1579857528000},"source":"Crossref","is-referenced-by-count":0,"title":["A Simple Proof for a Forbidden Subposet Problem"],"prefix":"10.37236","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0683-1414","authenticated-orcid":false,"given":"Ryan R.","family":"Martin","sequence":"first","affiliation":[]},{"given":"Abhishek","family":"Methuku","sequence":"additional","affiliation":[]},{"given":"Andrew","family":"Uzzell","sequence":"additional","affiliation":[]},{"given":"Shanise","family":"Walker","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2020,1,24]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i1p31\/8018","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i1p31\/8018","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,24]],"date-time":"2020-01-24T09:18:48Z","timestamp":1579857528000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i1p31"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,24]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,1,9]]}},"URL":"https:\/\/doi.org\/10.37236\/7680","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,1,24]]},"article-number":"P1.31"}}