Three-pile Sharing Nim and the quadratic time winning strategy
We study a variant of 3-pile Nim in which a move consists of taking tokens from one pile and, instead of removing them, topping up on a smaller pile provided that the destination pile does not have more tokens than the source pile after the move. We discover a situation in which each column of two-d...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Ho, Nhan Bao [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2016transfer abstract |
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| Schlagwörter: |
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| Umfang: |
12 |
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| Übergeordnetes Werk: |
Enthalten in: Influence of bulk fibre properties of PAN-based carbon felts on their performance in vanadium redox flow batteries - Schweiss, Rüdiger ELSEVIER, 2015transfer abstract, the journal of the EATCS, Amsterdam [u.a.] |
|---|---|
| Übergeordnetes Werk: |
volume:646 ; year:2016 ; day:20 ; month:09 ; pages:49-60 ; extent:12 |
| Links: |
|---|
| DOI / URN: |
10.1016/j.tcs.2016.07.015 |
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ELV040056325 |
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| 520 | |a We study a variant of 3-pile Nim in which a move consists of taking tokens from one pile and, instead of removing them, topping up on a smaller pile provided that the destination pile does not have more tokens than the source pile after the move. We discover a situation in which each column of two-dimensional array of Sprague–Grundy values is a palindrome. We establish a formula for P -positions by which winning moves can be computed in quadratic time. We prove a formula for positions whose Sprague–Grundy values are 1 and estimate the distribution of those positions whose nim-values are g. We discuss the periodicity of nim-sequences that seem to be bounded. | ||
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10.1016/j.tcs.2016.07.015 doi GBVA2016010000017.pica (DE-627)ELV040056325 (ELSEVIER)S0304-3975(16)30349-8 DE-627 ger DE-627 rakwb eng 004 004 DE-600 620 VZ 690 VZ 50.92 bkl Ho, Nhan Bao verfasserin aut Three-pile Sharing Nim and the quadratic time winning strategy 2016transfer abstract 12 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier We study a variant of 3-pile Nim in which a move consists of taking tokens from one pile and, instead of removing them, topping up on a smaller pile provided that the destination pile does not have more tokens than the source pile after the move. We discover a situation in which each column of two-dimensional array of Sprague–Grundy values is a palindrome. We establish a formula for P -positions by which winning moves can be computed in quadratic time. We prove a formula for positions whose Sprague–Grundy values are 1 and estimate the distribution of those positions whose nim-values are g. We discuss the periodicity of nim-sequences that seem to be bounded. We study a variant of 3-pile Nim in which a move consists of taking tokens from one pile and, instead of removing them, topping up on a smaller pile provided that the destination pile does not have more tokens than the source pile after the move. We discover a situation in which each column of two-dimensional array of Sprague–Grundy values is a palindrome. We establish a formula for P -positions by which winning moves can be computed in quadratic time. We prove a formula for positions whose Sprague–Grundy values are 1 and estimate the distribution of those positions whose nim-values are g. We discuss the periodicity of nim-sequences that seem to be bounded. Combinatorial games Elsevier Nim Elsevier Sharing Nim Elsevier Quadratic time Elsevier Nim-sequence Elsevier Periodicity Elsevier Enthalten in Elsevier Schweiss, Rüdiger ELSEVIER Influence of bulk fibre properties of PAN-based carbon felts on their performance in vanadium redox flow batteries 2015transfer abstract the journal of the EATCS Amsterdam [u.a.] (DE-627)ELV013125583 volume:646 year:2016 day:20 month:09 pages:49-60 extent:12 https://doi.org/10.1016/j.tcs.2016.07.015 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_22 GBV_ILN_40 50.92 Meerestechnik VZ AR 646 2016 20 0920 49-60 12 045F 004 |
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10.1016/j.tcs.2016.07.015 doi GBVA2016010000017.pica (DE-627)ELV040056325 (ELSEVIER)S0304-3975(16)30349-8 DE-627 ger DE-627 rakwb eng 004 004 DE-600 620 VZ 690 VZ 50.92 bkl Ho, Nhan Bao verfasserin aut Three-pile Sharing Nim and the quadratic time winning strategy 2016transfer abstract 12 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier We study a variant of 3-pile Nim in which a move consists of taking tokens from one pile and, instead of removing them, topping up on a smaller pile provided that the destination pile does not have more tokens than the source pile after the move. We discover a situation in which each column of two-dimensional array of Sprague–Grundy values is a palindrome. We establish a formula for P -positions by which winning moves can be computed in quadratic time. We prove a formula for positions whose Sprague–Grundy values are 1 and estimate the distribution of those positions whose nim-values are g. We discuss the periodicity of nim-sequences that seem to be bounded. We study a variant of 3-pile Nim in which a move consists of taking tokens from one pile and, instead of removing them, topping up on a smaller pile provided that the destination pile does not have more tokens than the source pile after the move. We discover a situation in which each column of two-dimensional array of Sprague–Grundy values is a palindrome. We establish a formula for P -positions by which winning moves can be computed in quadratic time. We prove a formula for positions whose Sprague–Grundy values are 1 and estimate the distribution of those positions whose nim-values are g. We discuss the periodicity of nim-sequences that seem to be bounded. Combinatorial games Elsevier Nim Elsevier Sharing Nim Elsevier Quadratic time Elsevier Nim-sequence Elsevier Periodicity Elsevier Enthalten in Elsevier Schweiss, Rüdiger ELSEVIER Influence of bulk fibre properties of PAN-based carbon felts on their performance in vanadium redox flow batteries 2015transfer abstract the journal of the EATCS Amsterdam [u.a.] (DE-627)ELV013125583 volume:646 year:2016 day:20 month:09 pages:49-60 extent:12 https://doi.org/10.1016/j.tcs.2016.07.015 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_22 GBV_ILN_40 50.92 Meerestechnik VZ AR 646 2016 20 0920 49-60 12 045F 004 |
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10.1016/j.tcs.2016.07.015 doi GBVA2016010000017.pica (DE-627)ELV040056325 (ELSEVIER)S0304-3975(16)30349-8 DE-627 ger DE-627 rakwb eng 004 004 DE-600 620 VZ 690 VZ 50.92 bkl Ho, Nhan Bao verfasserin aut Three-pile Sharing Nim and the quadratic time winning strategy 2016transfer abstract 12 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier We study a variant of 3-pile Nim in which a move consists of taking tokens from one pile and, instead of removing them, topping up on a smaller pile provided that the destination pile does not have more tokens than the source pile after the move. We discover a situation in which each column of two-dimensional array of Sprague–Grundy values is a palindrome. We establish a formula for P -positions by which winning moves can be computed in quadratic time. We prove a formula for positions whose Sprague–Grundy values are 1 and estimate the distribution of those positions whose nim-values are g. We discuss the periodicity of nim-sequences that seem to be bounded. We study a variant of 3-pile Nim in which a move consists of taking tokens from one pile and, instead of removing them, topping up on a smaller pile provided that the destination pile does not have more tokens than the source pile after the move. We discover a situation in which each column of two-dimensional array of Sprague–Grundy values is a palindrome. We establish a formula for P -positions by which winning moves can be computed in quadratic time. We prove a formula for positions whose Sprague–Grundy values are 1 and estimate the distribution of those positions whose nim-values are g. We discuss the periodicity of nim-sequences that seem to be bounded. Combinatorial games Elsevier Nim Elsevier Sharing Nim Elsevier Quadratic time Elsevier Nim-sequence Elsevier Periodicity Elsevier Enthalten in Elsevier Schweiss, Rüdiger ELSEVIER Influence of bulk fibre properties of PAN-based carbon felts on their performance in vanadium redox flow batteries 2015transfer abstract the journal of the EATCS Amsterdam [u.a.] (DE-627)ELV013125583 volume:646 year:2016 day:20 month:09 pages:49-60 extent:12 https://doi.org/10.1016/j.tcs.2016.07.015 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_22 GBV_ILN_40 50.92 Meerestechnik VZ AR 646 2016 20 0920 49-60 12 045F 004 |
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Three-pile Sharing Nim and the quadratic time winning strategy |
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Three-pile Sharing Nim and the quadratic time winning strategy |
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Ho, Nhan Bao |
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Influence of bulk fibre properties of PAN-based carbon felts on their performance in vanadium redox flow batteries |
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Influence of bulk fibre properties of PAN-based carbon felts on their performance in vanadium redox flow batteries |
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Ho, Nhan Bao |
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Elektronische Aufsätze |
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Ho, Nhan Bao |
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10.1016/j.tcs.2016.07.015 |
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004 620 690 |
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three-pile sharing nim and the quadratic time winning strategy |
| title_auth |
Three-pile Sharing Nim and the quadratic time winning strategy |
| abstract |
We study a variant of 3-pile Nim in which a move consists of taking tokens from one pile and, instead of removing them, topping up on a smaller pile provided that the destination pile does not have more tokens than the source pile after the move. We discover a situation in which each column of two-dimensional array of Sprague–Grundy values is a palindrome. We establish a formula for P -positions by which winning moves can be computed in quadratic time. We prove a formula for positions whose Sprague–Grundy values are 1 and estimate the distribution of those positions whose nim-values are g. We discuss the periodicity of nim-sequences that seem to be bounded. |
| abstractGer |
We study a variant of 3-pile Nim in which a move consists of taking tokens from one pile and, instead of removing them, topping up on a smaller pile provided that the destination pile does not have more tokens than the source pile after the move. We discover a situation in which each column of two-dimensional array of Sprague–Grundy values is a palindrome. We establish a formula for P -positions by which winning moves can be computed in quadratic time. We prove a formula for positions whose Sprague–Grundy values are 1 and estimate the distribution of those positions whose nim-values are g. We discuss the periodicity of nim-sequences that seem to be bounded. |
| abstract_unstemmed |
We study a variant of 3-pile Nim in which a move consists of taking tokens from one pile and, instead of removing them, topping up on a smaller pile provided that the destination pile does not have more tokens than the source pile after the move. We discover a situation in which each column of two-dimensional array of Sprague–Grundy values is a palindrome. We establish a formula for P -positions by which winning moves can be computed in quadratic time. We prove a formula for positions whose Sprague–Grundy values are 1 and estimate the distribution of those positions whose nim-values are g. We discuss the periodicity of nim-sequences that seem to be bounded. |
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| title_short |
Three-pile Sharing Nim and the quadratic time winning strategy |
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https://doi.org/10.1016/j.tcs.2016.07.015 |
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