[et_pb_section fb_built=”1″ make_equal=”on” use_custom_gutter=”on” gutter_width=”1″ specialty=”on” background_color_2=”gcid-e428b4a0-8f75-478b-bc91-d4c919946667″ padding_top_1=”0px” padding_top_2=”20px” padding_right_1=”0px” padding_right_2=”15px” padding_bottom_1=”0px” padding_bottom_2=”40px” padding_left_1=”0px” padding_left_2=”15px” padding_top_bottom_link_1=”false” padding_top_bottom_link_2=”false” padding_left_right_link_1=”false” padding_left_right_link_2=”false” _builder_version=”4.25.2″ _module_preset=”default” width=”100%” max_width=”100%” inner_width=”100%” inner_max_width=”100%” custom_margin=”0px|0px|0px|0px|false|false” custom_padding=”0px|0px|0px|0px|false|false” border_width_top=”7px” border_color_top=”gcid-e428b4a0-8f75-478b-bc91-d4c919946667″ locked=”off” global_colors_info=”{%22gcid-e428b4a0-8f75-478b-bc91-d4c919946667%22:%91%22border_color_top%22,%22background_color_2%22%93}”][et_pb_column type=”3_4″ specialty_columns=”3″ _builder_version=”4.16″ custom_padding=”|||” global_colors_info=”{}” custom_padding__hover=”|||”][et_pb_row_inner use_custom_gutter=”on” gutter_width=”1″ make_equal=”on” _builder_version=”4.25.2″ _module_preset=”default” width=”100%” max_width=”100%” custom_margin=”0px|0px|0px|0px|false|false” custom_padding=”40px|40px|10px|40px|false|false” global_colors_info=”{}”][et_pb_column_inner saved_specialty_column_type=”3_4″ _builder_version=”4.25.2″ _module_preset=”default” custom_padding=”0px|0px|0px|0px|false|false” global_colors_info=”{}”][et_pb_heading title=”Combinatorial Game Theory Colloquium V” _builder_version=”4.27.3″ _module_preset=”default” title_text_color=”#f29062″ title_font_size=”22px” global_colors_info=”{}”][\/et_pb_heading][et_pb_heading title=”(Lisbon, January 31 – February 2, 2025)” _builder_version=”4.27.3″ _module_preset=”default” title_level=”h6″ custom_margin=”-5px||||false|false” custom_padding=”0px||||false|false” locked=”off” global_colors_info=”{}”][\/et_pb_heading][et_pb_text _builder_version=”4.27.3″ _module_preset=”default” text_orientation=”justified” global_colors_info=”{}”]<\/p>\n
Combinatorial Game Theory<\/span><\/b>\u00a0(CGT) is a branch\u00a0of mathematics\u00a0<\/span><\/span>that focuses on the study of\u00a0<\/span><\/span>sequential games\u00a0with perfect information<\/span><\/b>.\u00a0<\/span><\/span>These games encompass\u00a0<\/span><\/span>well-known rulesets such as Amazons,\u00a0Clobber, Domineering, Hackenbush, Konane,\u00a0Nim, Octal Games, Wythoff\u2019s Nim.\u00a0<\/span>Following John Conway’s seminal work,<\/span>\u00a0On Numbers and Games\u00a0<\/i>(1976), Elwyn Berlekamp, John Conway, and Richard Guy\u00a0<\/span><\/span>authored\u00a0<\/span><\/span>\u00a0\u201cthe book\u201d\u00a0Winning Ways\u00a0<\/i>(1982)<\/span>\u00a0<\/span>, which presents a unified\u00a0<\/span><\/span>mathematical\u00a0theory t<\/span>o analyze a wide range of<\/span>\u00a0<\/span>combinatorial rulesets.\u00a0<\/span><\/span>Additionally,\u00a0<\/span><\/span>Lessons in Play<\/span><\/i>\u00a0(2007), by Michael Albert, David Wolfe, and Richard Nowakowski, and\u00a0Combinatorial Game Theory<\/i>\u00a0(2013), by Aaron Siegel<\/span>\u00a0<\/span>are essential readings on the subject.\u00a0<\/span><\/p>\n Combinatorial Game Theory Colloquia<\/span><\/strong>\u00a0are held every two years, in Portugal. Associa\u00e7\u00e3o Ludus will organize in Lisbon, Portugal, the fifth edition of the CGTC,\u00a0<\/span>January 31 – February 02, 2025<\/span><\/strong>,<\/span>\u00a0with support of Centro de Matem\u00e1tica Aplicada \u00e0 Previs\u00e3o e Decis\u00e3o Econ\u00f3mica, Centro de Matem\u00e1tica e Aplica\u00e7\u00f5es (NovaMath, FCT NOVA), and Sociedade Portuguesa de Matem\u00e1tica.\u00a0<\/span><\/p>\n The meeting will take place at\u00a0\u00a0<\/span>Faculdade de Ci\u00eancias e Tecnologia Universidade Nova de Lisboa<\/a>, Campus de Caparica, 2829-516 Caparica, Portugal.<\/span><\/p>\n See a map\u00a0<\/span>here<\/a>.<\/span><\/p>\n <\/span><\/p>\n [\/et_pb_text][et_pb_image src=”https:\/\/ludicum.org\/wp-content\/uploads\/2024\/11\/poster_cgtcV.jpg” title_text=”Screenshot” align=”center” _builder_version=”4.27.3″ _module_preset=”default” custom_padding=”||60px||false|false” global_colors_info=”{}”][\/et_pb_image][et_pb_text _builder_version=”4.27.3″ _module_preset=”default” custom_padding=”||30px||false|false” global_colors_info=”{}”]<\/p>\n For informations about submissions and registrations, just mail us:\u00a0<\/span>cgtc@cgtc.eu<\/a><\/span><\/strong><\/p>\n [\/et_pb_text][et_pb_text _builder_version=”4.27.4″ _module_preset=”default” global_colors_info=”{}”]<\/p>\n Standard Talks, Mornings (9:30-13:15)\u00a0 — Amphitheater 203 in Building IV<\/strong> <\/strong><\/p>\n [\/et_pb_text][et_pb_image src=”https:\/\/ludicum.org\/wp-content\/uploads\/2025\/03\/ProgramCGTCV-actualizado.png” title_text=”ProgramCGTCV-actualizado” align=”center” _builder_version=”4.27.4″ _module_preset=”default” custom_padding=”20px||||false|false” global_colors_info=”{}”][\/et_pb_image][et_pb_tabs _builder_version=”4.27.4″ _module_preset=”default” custom_margin=”20px||||false|false” global_colors_info=”{}”][et_pb_tab title=”Organization” _builder_version=”4.27.4″ _module_preset=”default” global_colors_info=”{}”]<\/p>\n <\/a>Aaron Siegel<\/a>, <\/strong>San Francisco, California Alda Carvalho<\/strong><\/a>,\u00a0<\/span>DCeT, ABERTA University & CEMAPRE-ISEG Research, ULISBOA<\/span> [\/et_pb_tab][et_pb_tab title=”Abstracts” _builder_version=”4.27.4″ _module_preset=”default” global_colors_info=”{}”]<\/p>\n Alda Carvalho<\/strong><\/b>, DCeT-Aberta University & CEMAPRE\/ISEG Research-University of Lisbon, Portugal<\/p>\n Title<\/strong><\/b>:\u00a0 Cyclic impartial games with carry-on moves (Part I<\/strong><\/b>)<\/p>\n Abstract<\/strong><\/b>: In an impartial combinatorial game, both players have the same options in the game and all its subpositions. The classical Sprague-Grundy Theory was developed for short impartial games, where players have a finite number of options, there are no special moves, and an infinite run is not possible. Subsequently, many generalizations have been proposed, particularly the Smith-Frankel-Perl Theory for games where the infinite run is possible, and the Larsson-Nowakowski-Santos Theory able of dealing with entailing moves.This talk presents a generalization that combines these two theories, making it suitable for analyzing cyclic impartial games with carry-on moves, which are particular cases of entailing moves where the entailed player has no freedom\u00a0of choice in their response.<\/p>\n (Joint work with Carlos Pereira dos Santos, Koki Suetsugu, Richard J. Nowakowski, Tomoaki Abuku, and Urban Larsson)<\/p>\n Alfie Davies<\/strong>,\u00a0Memorial University<\/span>, Canada<\/span><\/p>\n Title<\/strong><\/b>:\u00a0What if winning moves are banned?<\/span><\/p>\n Abstract<\/strong><\/b>: Learning the winning strategy for a game like Nim can make it less fun to play. But what if we play these games with the following alteration: we are not allowed to make a move which would have been winning before. Can we leverage our knowledge of the strategy for the original game to play this new paradigm well?<\/p>\n Ankita Dargad<\/strong>, Indian Institute of Technology Bombay, India<\/p>\n Title<\/strong><\/b>: Thermograph invariance for certain games<\/p>\n Abstract<\/strong><\/b>: In the context of disjunctive sums of combinatorial games, a natural question arises: Is it advantageous\u00a0to play first in a specific component? And if so, can this advantage be quantified? Temperature\u00a0theory seeks to answer this by measuring the incentive to move first. A key tool in this theory is the\u00a0thermograph – a geometric representation that often simplifies the computation of a game’s temperature.\u00a0For the Robin Hood game, an instance of the cumulative game: Wealth Nim (arXiv:2005.06326<\/a>), the\u00a0canonical forms become overwhelmingly large and lack discernible patterns. However, the thermographs\u00a0for Robin Hood reveal a surprising regularity, exhibiting only a limited number of shapes as the heap\u00a0sizes increase. This invariance was uncovered through an exploration of the monotonicity of the stops\u00a0of the game’s options and the evolving shapes of its thermographs. This discovery leads to a compelling\u00a0question: under what general conditions does this thermograph invariance hold?<\/p>\n (Joint work with\u00a0<\/strong><\/b>Urban Larsson and Niranjan Balachandran)<\/p>\n Anjali Bhagat<\/strong><\/b>, Indian Institute of Technology Bombay, India<\/p>\n Title<\/strong><\/b>: Fork positions and 2-dimensional toppling dominoes<\/p>\n Abstract<\/strong><\/b>: Toppling Dominoes is known as a one-dimensional combinatorial\u00a0game where the dominoes are arranged in a straight line. This project\u00a0introduces fork positions where the dominoes are placed in a 2-dimensional\u00a0plane. We define the rules for 2-dimensional fork positions in Toppling\u00a0Dominoes. We explore how fork positions are different from 1-dimensional\u00a0Toppling Dominoes. We prove that doubling a single domino to make the\u00a0position two-dimensional favors the player whose domino was doubled. The\u00a0game values become incomparable in the case of the neutral green domino.\u00a0We also prove that when we make two 1-dimensional games into a fork position\u00a0again, it favors the player whose domino was used to make the fork.<\/p>\n (Joint work with\u00a0<\/strong><\/b>Urban Larsson)<\/p>\n Balaji Rohidas Kadam<\/strong><\/b>,\u00a0 Indian Institute of Technology Madras, India<\/p>\n Title<\/strong><\/b>: Kotzig’s Nim under mis\u00e8re play<\/p>\n Abstract<\/strong><\/b>: We study Kotzig’s Nim game, a combinatorial game played on a directed\u00a0cycle with labeled vertices, inspired by the geography game. In Kotzig’s Nim,\u00a0two players take turns moving a token that starts at one node of the cycle, advancing it clockwise around a circular board of\u00a0n<\/em><\/i>\u00a0nodes based on a predefined set\u00a0of allowed step sizes M, a proper subset of natural numbers. Although Kotzig’s\u00a0Nim rules are easy to understand and have been around for several decades,\u00a0there are only a few known results.\u00a0All existing results regarding Kotzig’s nim have concentrated on identifying\u00a0P-positions in the normal play version – where the player who cannot make a\u00a0move loses. We investigate P-positions in the\u00a0mis\u00e8re\u00a0play version, where the\u00a0\u00a0player unable to move wins. We show that the game equivalence theorem applicable in normal play also applies to mis\u00e8re play. Our analysis mainly focuses on\u00a0move sets M consisting of two elements. We also establish some general results\u00a0about the winning player in the mis\u00e8re game \u0393(M={a<\/em><\/i>,a<\/em><\/i>+1};\u00a0n<\/em><\/i>).<\/p>\n (Joint work with Shaiju A. J.)<\/p>\n Bernhard von Stengel<\/strong>, London School of Economics, UK<\/p>\n Title<\/strong><\/b>: Combinatorial Game Theory Collection (IJGT)<\/p>\n Abstract<\/strong><\/b>: The International Journal of Game Theory (IJGT) is inviting submissions of significant papers in Combinatorial Game Theory. All articles are reviewed to the high standards of IJGT (one-sided blind peer review). Accepted papers are published online immediately after production, and are added to the CGT online Collection at\u00a0https:\/\/link.springer.com\/collections\/jhjdeifbdf<\/a>. Two editions of CGT papers have been and are about to be published in printed issues of IJGT, the first as Issue 2 of Volume 47 in 2018, the second as Issue 4 of Volume 53 in 2024.\u00a0The CGT Collection has been aligned with the editions of the Combinatorial Game Theory Colloquia. The special collection does not represent formal proceedings. IJGT welcomes high quality submissions related to works presented at the conference.\u00a0This brief talk serves to share some information and answer questions.<\/p>\n (Joint work with Carlos Pereira dos Santos and Urban Larsson)<\/p>\n Bojan Ba\u0161i\u0107<\/strong>,\u00a0 University of Novi Sad, Serbia<\/p>\n Title<\/strong><\/b>: Yet another (not so well-known) funny afternoon in a jail courtyard, and its (even less well-known) variation with quite unexpected consequences<\/p>\n Abstract<\/strong><\/b>:\u00a0There are many conundrums in circulation depicted as a game between prisoners and a warden. It is often the case that, in spite of their seemingly naive (cheerful?) presentation, there are deep mathematical theories that lurk beneath them. For some of them, however, it looks as though they remain just (light) brain-teasers and nothing more. As a warmer-upper, we present something from this latter class (which is, in contrast to Ebert’s\u00a0n<\/em><\/i>-prisoners puzzle, the hats-in-a-line game, etc., significantly lesser known). We then ask the same question for a slight variation of the same problem. Think very conscientiously before trying to guess the answer, it is very likely that you will be wrong!<\/p>\n Carlos Pereira dos Santos<\/strong><\/b>, Center for Mathematics and Applications (NOVA Math), FCT NOVA, Portugal<\/p>\n Title<\/strong><\/b>:\u00a0 Cyclic impartial games with carry-on moves (Part II<\/strong><\/b>)<\/p>\n Abstract<\/strong><\/b>: Look at Alda Carvalho’s abstract.<\/p>\n (Joint work with Alda Carvalho, Koki Suetsugu, Richard J. Nowakowski, Tomoaki Abuku, and Urban Larsson)<\/p>\n Craig Tennenhouse<\/strong><\/b>, University of New England, USA<\/p>\n Title<\/strong><\/b>: Temperature of Partizan Arc Kayles<\/p>\n Abstract<\/strong><\/b>: Motivated by the longstanding conjecture that the temperature of Domineering is bounded by two we examine Partizan Arc Kayles as a generalization, and show that this game has unbounded temperature on trees.<\/p>\n (Joint work with\u00a0Svenja Huntemann and Neil McKay)<\/p>\n Craig Tennenhouse<\/strong><\/b>, University of New England, USA and\u00a0Kyle Burke<\/strong>, Florida Southern College, USA<\/p>\n Title<\/strong><\/b>: A CGT Book for early undergraduates<\/p>\nREGISTRATION<\/span><\/h5>\n
PROGRAM<\/span><\/h5>\n
Working Sessions, Afternoons (15:00-18:00) —\u00a0Rooms 112 and 115, and Amphitheater 202 in Building IV<\/strong><\/b><\/span><\/p>\n
List of participants:\u00a0<\/strong><\/b>Alda Carvalho, Alfie Davies, Anjali Bhagat, Ankita Dargad, Balaji Rohidas Kadam, Bernhard von Stengel, Bojan Ba\u0161i\u0107, Carlos Pereira dos Santos, Colin Wright,\u00a0<\/span>Craig Tennenhouse, Dennis Clemens, Ethan Saunders, Fran\u00e7ois Carret, Harman Agrawal, Hideki Tsuiki, Hikaru Manabe, Hiroki Inazu, Hironori Kiya, Hiyu Inoue, Jo\u00e3o Pedro Neto,\u00a0<\/span>Jorge Nuno Silva, Kanae Yoshiwatari, Koki Suetsugu, Kosaku Watanabe, Kyle Burke, Luka Sen, Martin Mueller, Mathieu Dufour, Michael Fisher, Milos Stojakovic,\u00a0 Nikolina Miholjcic, Nina Miholjcic, Paul Ellis,\u00a0<\/span>Prem Kant, Radojka Ciganovi\u0107, Richard Nowakowski, Ryan Dinh, Shun-ichi Kimura,\u00a0 Svenja Huntemann, Takahiro Yamashita, Thotsaporn Aek Thanitapinonda, Tiago Hirth,\u00a0<\/span>Tomoaki Abuku, Urban Larsson, Vlado Uljarevi\u0107, Vuka\u0161in \u0110inovi\u0107, Yannick Mogge.<\/span><\/p>\nScientific Committee<\/h3>\n
<\/a>Alda Carvalho<\/a>,\u00a0<\/strong>DCeT, ABERTA University & CEMAPRE-ISEG Research, ULISBOA
<\/a>Bernhard von Stengel<\/a>, <\/strong>London School of Economics and Political Science
Carlos Pereira dos Santos<\/a>, <\/strong>Center for Mathematics and Applications (NovaMath), FCT NOVA
Eric Duchene<\/a>, <\/strong>IUT Lyon 1, LIRIS lab.
Jo\u00e3o Pedro Neto<\/a>, <\/strong>University of Lisbon
Jorge Nuno Silva<\/a>, <\/strong>University of Lisbon
Koki Suetsugu<\/a>, <\/strong>Waseda University
Milos Stojakovic<\/a>, <\/strong>University of Novi Sad
Richard Nowakowski<\/a>, <\/strong>Dalhousie University
Urban Larsson<\/a>, <\/strong>Indian Institute of Technology Bombay<\/span><\/p>\n<\/ul>\n
Organizing Committee<\/h3>\n
Carlos Pereira dos Santos<\/strong><\/a>, Center for Mathematics and Applications (NovaMath), FCT NOVA<\/span>
Jorge Nuno Silva<\/strong><\/a>,<\/strong> University of Lisbon<\/span>
Tiago Hirth<\/strong><\/a>, Ludus Association<\/span><\/p>\n