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Some Properties of Pomax Games.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2014 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

We study pomax games, a family of combinatorial games which are always integer-valued.

Specifically, we study games played on Young diagrams and Boolean lattices. We find a linear

algorithm for computing the values of pomax games played on Young diagrams with only two

rows. Some of the statements involved in this proof hold also for games on general Young

diagrams.

For pomax games on Boolean lattices, we introduce the concept of upper and lower games and use that as a tool to study the distribution of possible game values. We prove that games that equal any sufficiently small even integer can always be found, and that the density of distinct game values converges when the game size tends to infinity. Based on computational evidence, we conjecture that if the upper and lower games of some game are identical, then the value of that game is the sum of the upper and lower game.

Abstract [sv]

Vi studerar pomaxspel, en familj av heltalsvärda kombinatoriska spel. Mer specifikt studerar vi dessa spel då de spelas på Youngdiagram och Boolska lattis. Vi hittar en linjär algoritm för att beräkna värdet av pomaxspel på Youngdiagram med som mest två rader. Vissa av de ingående resultaten håller även for spel på allmänna Youngdiagram.

Gällande pomaxspel pa Boolska lattis introducerar vi koncepten övre och undre spel, och

använder detta for att analysera fördelningen av möjliga spelvärden. Vi visar att det alltid

finns spel av varje tillräckligt litet jämnt värde, och att densiteten av distinkta spelvärden konvergerar då spelstorleken går mot oändligheten. Baserat på beräkningar förmodar vi att om det övre och undre spelet hörande till något spel ar identiska, så är detta spel lika med summan av det övre och undre spelet.

Place, publisher, year, edition, pages
2014. , 35 p.
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:kth:diva-147692OAI: oai:DiVA.org:kth-147692DiVA: diva2:731812
Supervisors
Available from: 2014-07-02 Created: 2014-07-02 Last updated: 2014-07-02Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
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