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Alexey Ustinov
Alexey Ustinov
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This is my latest attempt to simplify an old problem of mine so much that the simplified problem can actually be answered.

Starting with the generating function for unrestricted partitions:

$$(1+x+x^2+x^3+\ldots)(1+x^2+x^4+x^6+\ldots)(1+x^3+x^6+x^9)\ldots$$$$(1+x+x^2+x^3+\ldots)(1+x^2+x^4+x^6+\ldots)(1+x^3+x^6+x^9+\ldots)\ldots$$

Change some of the plus signs in the leftmost expression in parentheses to minus signs. Is it possible that the resulting series has coefficients all of which are $1$, $-1$, or zero?

I believe that the answer is no, but I'm not convinced by my computer aided search.

This is my latest attempt to simplify an old problem of mine so much that the simplified problem can actually be answered.

Starting with the generating function for unrestricted partitions:

$$(1+x+x^2+x^3+\ldots)(1+x^2+x^4+x^6+\ldots)(1+x^3+x^6+x^9)\ldots$$

Change some of the plus signs in the leftmost expression in parentheses to minus signs. Is it possible that the resulting series has coefficients all of which are $1$, $-1$, or zero?

I believe that the answer is no, but I'm not convinced by my computer aided search.

This is my latest attempt to simplify an old problem of mine so much that the simplified problem can actually be answered.

Starting with the generating function for unrestricted partitions:

$$(1+x+x^2+x^3+\ldots)(1+x^2+x^4+x^6+\ldots)(1+x^3+x^6+x^9+\ldots)\ldots$$

Change some of the plus signs in the leftmost expression in parentheses to minus signs. Is it possible that the resulting series has coefficients all of which are $1$, $-1$, or zero?

I believe that the answer is no, but I'm not convinced by my computer aided search.

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Alexey Ustinov
Alexey Ustinov
  • 12.3k
  • 7
  • 87
  • 119

This is my latest attempt to simplify an old problem of mine so much that the simplified problem can actually be answered.

Starting with the generating function for unrestricted partitions:

(1+x+x^2+x^3+...)(1+x^2+x^4+x^6+...)(1+x^3+x^6+x^9)...$$(1+x+x^2+x^3+\ldots)(1+x^2+x^4+x^6+\ldots)(1+x^3+x^6+x^9)\ldots$$

Change some of the plus signs in the leftmost expression in parentheses to minus signs. Is it possible that the resulting series has coefficients all of which are 1, -1$1$, $-1$,or or zero?

I believe that the answer is no, but I'm not convinced by my computer aided search.

This is my latest attempt to simplify an old problem of mine so much that the simplified problem can actually be answered.

Starting with the generating function for unrestricted partitions:

(1+x+x^2+x^3+...)(1+x^2+x^4+x^6+...)(1+x^3+x^6+x^9)...

Change some of the plus signs in the leftmost expression in parentheses to minus signs. Is it possible that the resulting series has coefficients all of which are 1, -1 ,or zero?

I believe that the answer is no, but I'm not convinced by my computer aided search.

This is my latest attempt to simplify an old problem of mine so much that the simplified problem can actually be answered.

Starting with the generating function for unrestricted partitions:

$$(1+x+x^2+x^3+\ldots)(1+x^2+x^4+x^6+\ldots)(1+x^3+x^6+x^9)\ldots$$

Change some of the plus signs in the leftmost expression in parentheses to minus signs. Is it possible that the resulting series has coefficients all of which are $1$, $-1$, or zero?

I believe that the answer is no, but I'm not convinced by my computer aided search.

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David S. Newman
David S. Newman
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A simplified version of an old problem about the generating function for unrestricted partitions

This is my latest attempt to simplify an old problem of mine so much that the simplified problem can actually be answered.

Starting with the generating function for unrestricted partitions:

(1+x+x^2+x^3+...)(1+x^2+x^4+x^6+...)(1+x^3+x^6+x^9)...

Change some of the plus signs in the leftmost expression in parentheses to minus signs. Is it possible that the resulting series has coefficients all of which are 1, -1 ,or zero?

I believe that the answer is no, but I'm not convinced by my computer aided search.