Timeline for What is the generalization of the formula for Chung and Feller's Theorem 2 to odd numbers of steps?
Current License: CC BY-SA 4.0
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| Dec 18, 2023 at 19:16 | history | edited | Ira Gessel | CC BY-SA 4.0 |
fixed typo
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| Jan 2, 2022 at 5:35 | comment | added | Ira Gessel | Incidentally, this other interpretation of $\frac{j}{2(j+k)}\binom {2j}{j}\binom{2k}{k}$ has been published. It appears in my paper Super Ballot Numbers, sciencedirect.com/science/article/pii/0747717192900342, section 7. | |
| Jan 1, 2022 at 14:25 | comment | added | Shannon Starr | Thanks! In your slides (Gessel's slides) you also noted this is also ``the number of paths with m+n up steps and m+n-1 down steps whose last return to the x-axis is before the point (2m,0).'' So I think that may give an answer to my question, since the number of non-negative paths ending at a particular spot was also enumerated in Feller. It may give a different sum, partitioning on the last return. Those slides based on your work with your students Aminil Huq (PhD) for the first half and Apratim Roy (Masters) for the second half are wonderful, especially because of the included figures. | |
| Jan 1, 2022 at 14:12 | vote | accept | Shannon Starr | ||
| Dec 30, 2021 at 20:56 | history | edited | Ira Gessel | CC BY-SA 4.0 |
edited body
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| Dec 30, 2021 at 20:40 | history | answered | Ira Gessel | CC BY-SA 4.0 |