We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Published online by Cambridge University Press: 28 February 2011
Abstract. In a monotonic sequence game, two players alternately choose elements of a sequence from some fixed ordered set. The game ends when the resulting sequence contains either an ascending subsequence of length a or a descending one of length d. We investigate the behaviour of this game when played on finite linear orders or ℚ and provide some general observations for play on arbitrary ordered sets.
Introduction
Monotonic sequence games were introduced by Harary, Sagan and West in. We paraphrase the description of the rules as follows:
From a deck of cards labelled with the integers from 1 through n, two players take turns choosing a card and adding it to the right hand end of a row of cards. The game ends when there is a subsequence of a cards in the row whose values form an ascending sequence, or of d cards whose values form a descending sequence.
The parameters a, d, and n are set before the game begins. There are two possible methods for determining the winner of the game. In the normal form of the game, the winner is the player who places the last card (which forms an ascending or descending sequence of the required length). In the misère form of the game, that player is the loser. In these are called the achievement and avoidance forms of the game respectively.
To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.
