Patch is attached.
Ralf
On 10/24/25 14:02, Ralf Hemmecke wrote:
Ooops.
%%% (309) -> stirling1(0,0)$IntegerCombinatoricFunctions(Integer)
(309) 0
Type: Integer
That should be 1, right?
stirling1(n, m) ==
-- Definition: (-1)^(n-m) S[n, m] is the number of
-- permutations of n symbols which have m cycles.
n < 0 or m < 1 or m > n => 0
m = n => 1
S.Sn = n => coefficient(S.Sp, convert(m)@Z :: N)
x := monomial(1, 1)$SUP(I)
S.Sn := n
S.Sp := x
for k in 1 .. convert(n-1)@Z repeat S.Sp := S.Sp * (x - k::SUP(I))
coefficient(S.Sp, convert(m)@Z :: N)
It seems that the condition "m < 1" in the first line should only be
applied if n>0, i.e. it should be:
n < 0 or (n > 0 and m < 1) or m > n => 0
Probably the same problem in stirling2.
Ralf
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From 98709d5d73ddf373c22bae13aca9685b09aad52e Mon Sep 17 00:00:00 2001
From: Ralf Hemmecke <[email protected]>
Date: Sun, 9 Nov 2025 14:37:11 +0100
Subject: correct stirling1(0,0)=stirling2(0,0)=1
---
src/algebra/combinat.spad | 2 ++
1 file changed, 2 insertions(+)
diff --git a/src/algebra/combinat.spad b/src/algebra/combinat.spad
index 18ac0dee..17452892 100644
--- a/src/algebra/combinat.spad
+++ b/src/algebra/combinat.spad
@@ -157,6 +157,7 @@ IntegerCombinatoricFunctions(I : IntegerNumberSystem) : with
stirling1(n, m) ==
-- Definition: (-1)^(n-m) S[n, m] is the number of
-- permutations of n symbols which have m cycles.
+ zero? n and zero? m => 1
n < 0 or m < 1 or m > n => 0
m = n => 1
S.Sn = n => coefficient(S.Sp, convert(m)@Z :: N)
@@ -169,6 +170,7 @@ IntegerCombinatoricFunctions(I : IntegerNumberSystem) : with
stirling2(n, m) ==
-- definition: SS[n, m] is the number of ways of partitioning
-- a set of n elements into m non-empty subsets
+ zero? n and zero? m => 1
n < 0 or m < 1 or m > n => 0
m = 1 or n = m => 1
s : I := if odd? m then -1 else 1
--
2.43.0
