gh-40853: adding a note on Coxeter polynomials
    
about a very non-obvious property of the Coxeter polynomials of posets.

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- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about
- [x] I have updated the documentation and checked the documentation
preview.
    
URL: #40853
Reported by: Frédéric Chapoton
Reviewer(s):

Author: Release Manager

src/doc/en/reference/references/index.rst

@@ -4398,6 +4398,9 @@ REFERENCES:
 .. [Labelle2008] \G. Labelle. *New combinatorial computational methods
                  arising from pseudo-singletons.* DMTCS Proceedings 1, 2008.
 
+.. [Lad2021] S. Ladkani. *Refined Coxeter polynomials*, Proceedings ICRA 2020,
+             EMS Publishing House. :arxiv:`2110.15329`
+
 .. [Lak2010] Dan Laksov. *Splitting algebras and Gysin homomorphisms*.
              Journal of Commutative Algebra, Volume 2, Number 3, Fall 2010
 

src/sage/combinat/posets/posets.py

@@ -4391,6 +4391,15 @@ def coxeter_polynomial(self, algorithm="sage"):
         transformation. This polynomial only depends on the derived
         category of modules on the poset.
 
+        .. NOTE::
+
+            By Corollary 4.3 of [Lad2021]_, this polynomial does
+            not depend on the order of the ordinal summands.
+
+        .. SEEALSO::
+
+            :meth:`ordinal_sum`, :meth:`ordinal_summands`
+
         EXAMPLES::
 
             sage: P = posets.PentagonPoset()