Timeline for Checkmate in $\omega$ moves?
Current License: CC BY-SA 3.0
12 events
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| Jul 21, 2023 at 15:24 | comment | added | Joel David Hamkins | @NoamD.Elkies Is it possible to fix the ordinal notation? You don't mean $3\omega$ or $N\omega$ here, but rather $\omega 3$ and $\omega N$, or $\omega\cdot 3$ and $\omega\cdot N$, on this post and your other posts. As you know, ordinal multiplication is not commutative, and the notation has been standardized for over a century. The incorrect usage leads to confusion in discussion. | |
| Jun 18, 2018 at 10:18 | comment | added | Gabriel Nivasch | I don't completely understand the analysis. You say that, in a quarter-infinite board, after 1. ... Bf4 2. Rf2 Kc1 3. Rxf4, white can win in O(1) moves. But what prevents black from doing 3. ... Kd2 and continuing his escape to the northeast? | |
| May 3, 2011 at 20:35 | history | edited | Noam D. Elkies | CC BY-SA 3.0 |
See below for an explicit and improved construction of Mate in $N\omega$
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| May 3, 2011 at 18:41 | comment | added | Noam D. Elkies | Yes, that's the kind of thing I had in mind, except using the pattern p/p/p/p/p/p1p1p1p1p1p/PbPbPbPbPbPbP/p1p1p1p1p1p1p/P1P1P1P1P1P1P for the artificial corner (yours will work too). | |
| May 3, 2011 at 16:14 | comment | added | Junkie | Maybe pp2R3/pp1K4/pp2q3/pp1kb3/pppppppp/prprprpr/PpPpPpPp/1P1P1P1P for the $Z^2$ board, with the border patterns extended by some finite amount? White plays Rxe6, and attacks the Black bishop or checkmates, every move thereafter. Black cannot give up the bishop and still survive, if the finite extensions are elongated sufficiently. | |
| May 3, 2011 at 14:58 | comment | added | Junkie | I did screencapture from an "xboard" usage, and then clicked on the Image button (6th from left) on the toolbar under Your Answer when posting here. You need to upload the images to freeimagehosting.net or some similar portal. Having bigger than 8x8 would be useful too. | |
| May 3, 2011 at 14:47 | history | edited | Noam D. Elkies | CC BY-SA 3.0 |
added 218 characters in body
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| May 3, 2011 at 14:44 | comment | added | Noam D. Elkies | [Comment relocated to the right thread] \\ @Q.Yuan: Thanks for the Welcome message :-) \\ @Junkie: It's close. Having two pinned Rooks on the column helps. I think I see how to make it work now, and with a bounded number of pieces independent of the multiple of $\omega$. How did you post the chess diagrams here? I could give a link like janko.at/Retros/d.php?ff=B3p3/1rp1P3/... [Use the entire FEN; Mathoverflow won't show the full URL :-(], but that's probably poor form. | |
| May 3, 2011 at 3:20 | history | edited | Noam D. Elkies | CC BY-SA 3.0 |
Changed "K+B vs. K+R" twice to "K+R vs. K+B" which is clearer
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| May 1, 2011 at 22:29 | comment | added | Junkie | Does something like B3p3/1rp1P3/prk1P3/prp1P3/B1RpP3/3P4 work for the pinned rook(s), with the White c-pawn starting N squares below the picture? Then the White King cannot ferry across the b-file, so by starting it to the east and putting half-shells around the right side, this could work. EDIT: I guess not, for the free Black rook goes to the b-file, rather than checking, and can attack the c-pawn from it. | |
| May 1, 2011 at 22:04 | comment | added | Qiaochu Yuan | Welcome to MO, Dr. Elkies! | |
| May 1, 2011 at 21:49 | history | answered | Noam D. Elkies | CC BY-SA 3.0 |