Timeline for Relation between a continued fraction and partitions
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| S Feb 16, 2018 at 18:22 | history | bounty ended | CommunityBot | ||
| S Feb 16, 2018 at 18:22 | history | notice removed | CommunityBot | ||
| Feb 15, 2018 at 1:57 | comment | added | Luca Ghidelli | I am no expert, but there should be some works of Flajolet about combinatorial interpretations for continued fractions. In general, Henkel determinants, continued fractions and orthogonal polynomials are precisely related to each other and in turn they are related (e.g. via the Gessel-Lindstrom-Viennot lemma) to combinatorics, more precisely to weighted Motzkin paths. Sometimes Motzkin paths are related to partitions (see Mansour-Shattuck work), but I don't know enough. By the way I think that the interpretation of non-squashing partitions as binary partitions suits better the problem here. | |
| S Feb 8, 2018 at 16:48 | history | bounty started | Johann Cigler | ||
| S Feb 8, 2018 at 16:48 | history | notice added | Johann Cigler | Authoritative reference needed | |
| Feb 8, 2018 at 16:48 | history | edited | Johann Cigler | CC BY-SA 3.0 |
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| Feb 6, 2018 at 12:30 | comment | added | Johann Cigler | @Gerry Myerson: Sorry for the typo in your name. But the website has not allowed me to edit my comment. | |
| Feb 6, 2018 at 12:21 | comment | added | Johann Cigler | @Gerry Myersaon and Alexey Ustinov: I have looked at these links but have not seen any real connection with non-squashing partitions. The only connection seems to be that the non-squashing partitions modulo $2$ give the same values as $T_n.$ What I really want to know: Is this a lucky chance because they obey the same recursions or is there a proof where these partitions play an essential role? | |
| Feb 6, 2018 at 12:05 | comment | added | Johann Cigler | @Pietro Majer: Thank you for this information. But I am only interested in this specific continued fraction which is related to the Hankel determinants of the sequence $(a_n),$ where $a_n=1$ if $n+2$ is a power of $2$ and $a_n=0$ else. | |
| Feb 6, 2018 at 9:02 | comment | added | Pietro Majer | Since $z^{2^k-1}=z^{2^0}z^{2^1}\dots z^{2^{k-1}}$, there is another immediate continued fraction given by the Euler continued fraction formula en.wikipedia.org/wiki/… | |
| Feb 6, 2018 at 6:01 | comment | added | Alexey Ustinov | A088567 gives more links. | |
| Feb 6, 2018 at 5:55 | history | edited | Alexey Ustinov | CC BY-SA 3.0 |
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| Feb 5, 2018 at 22:39 | comment | added | Gerry Myerson | oeis.org/A090678 links to two papers on "non-squashing partitions". Was there nothing useful at those links? | |
| Feb 5, 2018 at 17:10 | history | asked | Johann Cigler | CC BY-SA 3.0 |