From bd28efb16b9fbd0e50c89fcca2ebf1ce37af2985 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?= Date: Fri, 19 Sep 2025 20:58:34 +0200 Subject: [PATCH] adding a note on Coxeter polynomials --- src/doc/en/reference/references/index.rst | 3 +++ src/sage/combinat/posets/posets.py | 9 +++++++++ 2 files changed, 12 insertions(+) diff --git a/src/doc/en/reference/references/index.rst b/src/doc/en/reference/references/index.rst index afe2e8dd43d..fa8671010aa 100644 --- a/src/doc/en/reference/references/index.rst +++ b/src/doc/en/reference/references/index.rst @@ -4387,6 +4387,9 @@ 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 diff --git a/src/sage/combinat/posets/posets.py b/src/sage/combinat/posets/posets.py index 0754db0a0f4..ec3353165af 100644 --- a/src/sage/combinat/posets/posets.py +++ b/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()