ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Mon, 30 Aug 2021 08:37:03 +0200Obtaining a poset of plane partitions via Sagehttps://ask.sagemath.org/question/58735/obtaining-a-poset-of-plane-partitions-via-sage/In Sage there is the command YoungsLatticePrincipalOrderIdeal(p)
to obtain the lattice of partitions contained in p (via Ferrer diagrams) with maximal element p.
My question is whether there is the same command for obtaining via Sage the finite poset of all plane partitions that are contained in a given plane partition p ?
(see https://en.wikipedia.org/wiki/Plane_partition )
edit: It would also be interesting how to obtain the poset of plane partitions of $m$ for a given $m \leq n$ as one can do the same for the Young lattice in Sage via P=posets.YoungsLattice(5).
Thank you for any help.Sun, 29 Aug 2021 17:12:52 +0200https://ask.sagemath.org/question/58735/obtaining-a-poset-of-plane-partitions-via-sage/Answer by FrédéricC for <p>In Sage there is the command YoungsLatticePrincipalOrderIdeal(p)
to obtain the lattice of partitions contained in p (via Ferrer diagrams) with maximal element p.</p>
<p>My question is whether there is the same command for obtaining via Sage the finite poset of all plane partitions that are contained in a given plane partition p ?</p>
<p>(see <a href="https://en.wikipedia.org/wiki/Plane_partition">https://en.wikipedia.org/wiki/Plane_p...</a> )</p>
<p>edit: It would also be interesting how to obtain the poset of plane partitions of $m$ for a given $m \leq n$ as one can do the same for the Young lattice in Sage via P=posets.YoungsLattice(5).</p>
<p>Thank you for any help.</p>
https://ask.sagemath.org/question/58735/obtaining-a-poset-of-plane-partitions-via-sage/?answer=58736#post-id-58736Like this
sage: def PP(a,b,c):
....: return posets.ProductOfChains([a,b,c]).order_ideals_lattice()
sage: PP(2,2,2)
Finite lattice containing 20 element
for the full poset. Then you can take any principal order filter.
**EDIT** Another way:
sage: P = PlanePartitions([4,3,2])
sage: q = P.random_element()
sage: qt = q.to_tableau()
sage: Poset(([x.to_tableau() for x in P if x.to_tableau() <= qt] ,lambda x,y: x<=y))
Finite poset containing 459 elements
Sun, 29 Aug 2021 17:50:45 +0200https://ask.sagemath.org/question/58735/obtaining-a-poset-of-plane-partitions-via-sage/?answer=58736#post-id-58736Comment by FrédéricC for <p>Like this</p>
<pre><code>sage: def PP(a,b,c):
....: return posets.ProductOfChains([a,b,c]).order_ideals_lattice()
sage: PP(2,2,2)
Finite lattice containing 20 element
</code></pre>
<p>for the full poset. Then you can take any principal order filter.</p>
<p><strong>EDIT</strong> Another way:</p>
<pre><code>sage: P = PlanePartitions([4,3,2])
sage: q = P.random_element()
sage: qt = q.to_tableau()
sage: Poset(([x.to_tableau() for x in P if x.to_tableau() <= qt] ,lambda x,y: x<=y))
Finite poset containing 459 elements
</code></pre>
https://ask.sagemath.org/question/58735/obtaining-a-poset-of-plane-partitions-via-sage/?comment=58751#post-id-58751Not clear what you want. See also https://doc.sagemath.org/html/en/reference/combinat/sage/combinat/plane_partition.htmlMon, 30 Aug 2021 08:37:03 +0200https://ask.sagemath.org/question/58735/obtaining-a-poset-of-plane-partitions-via-sage/?comment=58751#post-id-58751Comment by klaaa for <p>Like this</p>
<pre><code>sage: def PP(a,b,c):
....: return posets.ProductOfChains([a,b,c]).order_ideals_lattice()
sage: PP(2,2,2)
Finite lattice containing 20 element
</code></pre>
<p>for the full poset. Then you can take any principal order filter.</p>
<p><strong>EDIT</strong> Another way:</p>
<pre><code>sage: P = PlanePartitions([4,3,2])
sage: q = P.random_element()
sage: qt = q.to_tableau()
sage: Poset(([x.to_tableau() for x in P if x.to_tableau() <= qt] ,lambda x,y: x<=y))
Finite poset containing 459 elements
</code></pre>
https://ask.sagemath.org/question/58735/obtaining-a-poset-of-plane-partitions-via-sage/?comment=58738#post-id-58738Thank you. Sorry I do not fully understand you answer. For example how to obtain the poset of all plane partitions of $m$ with $m \leq n$ for a given $n$? Is it obtained by taking all your posets as in your answer with $a+b+c \leq n$?Sun, 29 Aug 2021 18:33:03 +0200https://ask.sagemath.org/question/58735/obtaining-a-poset-of-plane-partitions-via-sage/?comment=58738#post-id-58738