Timeline for Enumeration Result
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 9, 2012 at 12:27 | comment | added | Patricia Hersh | Agreed. For anyone here who hasn't seen this stuff, an excellent reference on generating functions satisfying algebraic and differential equations is Enumerative Combinatorics, Volume II, chapters 5 and 6, by Richard Stanley. | |
| May 9, 2012 at 4:16 | comment | added | Hugh Denoncourt | I interpreted the OP's wording as something like, "Suppose I derive an explicit generating function for a sequence, but I don't derive a closed form expression for the coefficients. Is it considered an enumeration of the sequence?" It is not hard to find examples in the enumerative literature where only the generating function is given. | |
| May 9, 2012 at 0:42 | comment | added | Patricia Hersh | Recurrence wasn't really the right word to use. I meant an algebraic equation or differential equation or something like that. For instance, the generating function for Catalan numbers satisfies a degree two algebraic equation that reflects the relationship $C_{n+1} = \sum_{i=0}^n C_i C_{n-i}$. | |
| May 8, 2012 at 23:25 | comment | added | Gerry Myerson | It's not clear at all what OP means by "an equation for a generating function", but I don't see how a function (as opposed to a sequence) can satisfy a recurrence. | |
| May 8, 2012 at 22:49 | comment | added | Patricia Hersh | I may have misunderstood the posting -- I was thinking the poster was saying that he or she didn't have a closed form for the generating function, but rather had a recurrence it satisfies. It seems quite safe to me to call a closed form for a generating function an enumeration. | |
| May 8, 2012 at 21:07 | comment | added | Hugh Denoncourt | Also, I hesitate to make a blanket statement, but, generating functions are usually regarded as an excellent form for an enumerative result. | |
| May 8, 2012 at 21:05 | history | answered | Hugh Denoncourt | CC BY-SA 3.0 |