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Daniel Parry
Daniel Parry
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Factorial Sums over Compositions or ``Unlabeled Permutations"

Let $C_n$ denote subset of integer compositions of $n$ and $c=(c_1,c_2,\dots c_n)$

In a divergent sum, the sequence $$ a_n=\sum_{c\in C_n} \prod_{c_i\in c} c_i! $$ frequently shows up and one expects it to be asymptotic to the contributions containing its maximal part. I just want to know if this kind of integer composition has been studied and if I can find some explicit estimates/bounds for it that already exist in the literature.

Edit: OEIS has the standard case linked as A051296. I am trying to look for the proper "google term" to get the generalization of this sum.

Factorial Sums over Compositions

Let $C_n$ denote subset of integer compositions of $n$ and $c=(c_1,c_2,\dots c_n)$

In a divergent sum, the sequence $$ a_n=\sum_{c\in C_n} \prod_{c_i\in c} c_i! $$ frequently shows up and one expects it to be asymptotic to the contributions containing its maximal part. I just want to know if this kind of integer composition has been studied and if I can find some explicit estimates/bounds for it that already exist in the literature.

Factorial Sums over Compositions or ``Unlabeled Permutations"

Let $C_n$ denote subset of integer compositions of $n$ and $c=(c_1,c_2,\dots c_n)$

In a divergent sum, the sequence $$ a_n=\sum_{c\in C_n} \prod_{c_i\in c} c_i! $$ frequently shows up and one expects it to be asymptotic to the contributions containing its maximal part. I just want to know if this kind of integer composition has been studied and if I can find some explicit estimates/bounds for it that already exist in the literature.

Edit: OEIS has the standard case linked as A051296. I am trying to look for the proper "google term" to get the generalization of this sum.

Source Link
Daniel Parry
Daniel Parry
  • 1.3k
  • 1
  • 15
  • 22

Factorial Sums over Compositions

Let $C_n$ denote subset of integer compositions of $n$ and $c=(c_1,c_2,\dots c_n)$

In a divergent sum, the sequence $$ a_n=\sum_{c\in C_n} \prod_{c_i\in c} c_i! $$ frequently shows up and one expects it to be asymptotic to the contributions containing its maximal part. I just want to know if this kind of integer composition has been studied and if I can find some explicit estimates/bounds for it that already exist in the literature.