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    <title>isSperner -- determines if a ranked poset has the Sperner property</title>
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o2 = true</code></pre>
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              <pre><code class="language-macaulay2">i3 : isSperner booleanLattice n

o3 = true</code></pre>
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          <p>However, the following poset is non-Sperner as it has an antichain of size $4$ but the set of elements of rank $0$ and the set of elements of rank $1$ are both of size $3$.</p>
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              <pre><code class="language-macaulay2">i4 : P = poset {{1,4}, {1,5}, {1,6}, {2,6}, {3,6}};</code></pre>
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              <pre><code class="language-macaulay2">i5 : isSperner P

o5 = false</code></pre>
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              <pre><code class="language-macaulay2">i6 : isAntichain(P, {2,3,4,5})

o6 = true</code></pre>
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              <pre><code class="language-macaulay2">i7 : rankGeneratingFunction P

o7 = 3q + 3

o7 : ZZ[q]</code></pre>
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        <h2>See also</h2>
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          <li><span><a title="computes the Dilworth number of a poset" href="_dilworth__Number.html">dilworthNumber</a> -- computes the Dilworth number of a poset</span></li>
          <li><span><a title="determines if a poset is ranked" href="_is__Ranked.html">isRanked</a> -- determines if a poset is ranked</span></li>
          <li><span><a title="determines if a ranked poset has the strict Sperner property" href="_is__Strict__Sperner.html">isStrictSperner</a> -- determines if a ranked poset has the strict Sperner property</span></li>
          <li><span><a title="computes all maximal antichains of a poset" href="_maximal__Antichains.html">maximalAntichains</a> -- computes all maximal antichains of a poset</span></li>
          <li><span><a title="computes the rank function of a ranked poset" href="_rank__Function.html">rankFunction</a> -- computes the rank function of a ranked poset</span></li>
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          <h2>Ways to use <span class="tt">isSperner</span>:</h2>
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            <li><kbd>isSperner(Poset)</kbd></li>
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          <h2>For the programmer</h2>
          <p>The object <a title="determines if a ranked poset has the Sperner property" href="_is__Sperner.html">isSperner</a> is <span>a <a title="a type of method function" href="../../Macaulay2Doc/html/___Method__Function.html">method function</a></span>.</p>
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        <div class="waystouse">
          <p>The source of this document is in <span class="tt">Posets.m2:6052:0</span>.</p>
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