Companion Relationships
The white edge between two companions means they don't like each other, for the party with no conflicts we don't want to have any adjacent companions in the party, so what we need to do is find all the maximum independent sets of the dislike-graph. (Orange arrows stand for likes)
Definitions:
A stable party is a group of people whose all members either
1.have no person they dislike in the group, or
2.have exactly one disliked person in the group while also having a person that they like.
A maximum stable party is a stable party that for any people that not in the party, if we add him/her to the party, the party will become unstable.
A strictly stable party is a stable party whose members have no one they dislike in the group (any independent set of the dislike-graph)
A maximum strictly stable party is a strictly stable party that for any people that not in the party, if we add him/her to the party, the party will become not strictly stable. (any maximum independent set of the dislike-graph)
A raiding party is a party that no one in the party will be unhappy if you rob a village.
There are 85 maximum strictly stable parties in M&B native, and another thing is to find out all the maximum stable parties that not strictly stable, where M&B wiki did listed all 10 member parties and 9 member parties (but some of them are not maximum), also there could be 8 member parties etc.
Groups With No Conflicts
Small circle group(Total: 5)
a: Alayen, Katrin (rotate 0-2 times)
b: Alayen, Firentis, Baheshtur (rotate 0-1 times)
Big circle group(Total: 17):
c: Borcha, Artimenner, Matheld, Lezalit, Rolf (rotate 0-1 times)
d: Borcha, Jermus, Lezalit, Rolf (rotate 0-9 times)
e: Borcha, Jermus, Ymira, Rolf (rotate 0-4 times)
(Note: For example if we apply 1 rotation on b: Alayen, Firentis, Baheshtur, then we will get a new b: Nizar, Katrin, Marnid, and 0 rotation on b is just b itself.)
All Maximum Strictly Stable Parties
Select 1 of 5 from the small circle group and combine it with 1 of the 17 large circle groups repeatedly to get 85 results.
10 Companions Party (Maximum Stable But Not Strictly Stable)
(from M&B wiki)
1.Alayen Artimenner Baheshtur Borcha Bunduk Katrin Matheld Nizar Rolf Ymira
9 Companions Party (Maximum Stable But Not Strictly Stable)
(from M&B wiki)
1. Alayen Artimenner Baheshtur Borcha Firentis Jeremus Lezalit Rolf Ymira 2. Alayen Artimenner Baheshtur Deshavi Firentis Klethi Lezalit Matheld Rolf 3. Alayen Artimenner Baheshtur Deshavi Firentis Klethi Lezalit Rolf Ymira 4. Alayen Artimenner Borcha Firentis Jeremus Lezalit Marnid Rolf Ymira 5. Alayen Baheshtur Bunduk Katrin Klethi Matheld Nizar Rolf Ymira 6. Artimenner Bunduk Deshavi Katrin Klethi Lezalit Marnid Matheld Nizar 7. Baheshtur Borcha Firentis Jeremus Lezalit Marnid Matheld Nizar Rolf 8. Baheshtur Deshavi Firentis Jeremus Klethi Lezalit Matheld Nizar Rolf
8 Companions Party (Maximum Strictly Stable)
1.AlayenArtimennerBaheshturBorchaFirentisLezalitMatheldRolf2.AlayenBaheshturBundukDeshaviFirentisJeremusKlethiYmira3.ArtimennerBorchaKatrinLezalitMarnidMatheldNizarRolf4.BundukDeshaviJeremusKatrinKlethiMarnidNizarYmira
7 Companions Party (Maximum Strictly Stable)
1.AlayenArtimennerBaheshturBorchaBundukFirentisMatheld2.AlayenArtimennerBaheshturBorchaBundukFirentisYmira3.AlayenArtimennerBaheshturBorchaFirentisRolfYmira4.AlayenArtimennerBaheshturBundukDeshaviFirentisMatheld5.AlayenArtimennerBaheshturBundukDeshaviFirentisYmira6.AlayenArtimennerBaheshturDeshaviFirentisLezalitMatheld7.AlayenArtimennerBorchaKatrinLezalitMatheldRolf8.AlayenBaheshturBorchaBundukFirentisJeremusYmira9.AlayenBaheshturBorchaFirentisJeremusLezalitRolf10.AlayenBaheshturBorchaFirentisJeremusRolfYmira11.AlayenBaheshturBundukDeshaviFirentisKlethiMatheld12.AlayenBaheshturDeshaviFirentisJeremusKlethiLezalit13.AlayenBaheshturDeshaviFirentisKlethiLezalitMatheld14.AlayenBaheshturFirentisJeremusKlethiLezalitRolf15.AlayenBaheshturFirentisJeremusKlethiRolfYmira16.AlayenBaheshturFirentisKlethiLezalitMatheldRolf17.AlayenBundukDeshaviJeremusKatrinKlethiYmira18.ArtimennerBaheshturBorchaLezalitMatheldNizarRolf19.ArtimennerBorchaBundukKatrinMarnidMatheldNizar20.ArtimennerBorchaBundukKatrinMarnidNizarYmira21.ArtimennerBorchaFirentisLezalitMarnidMatheldRolf22.ArtimennerBorchaKatrinMarnidNizarRolfYmira23.ArtimennerBundukDeshaviKatrinMarnidMatheldNizar24.ArtimennerBundukDeshaviKatrinMarnidNizarYmira25.ArtimennerDeshaviKatrinLezalitMarnidMatheldNizar26.BaheshturBundukDeshaviJeremusKlethiNizarYmira27.BorchaBundukJeremusKatrinMarnidNizarYmira28.BorchaJeremusKatrinLezalitMarnidNizarRolf29.BorchaJeremusKatrinMarnidNizarRolfYmira30.BundukDeshaviFirentisJeremusKlethiMarnidYmira31.BundukDeshaviKatrinKlethiMarnidMatheldNizar32.DeshaviJeremusKatrinKlethiLezalitMarnidNizar33.DeshaviKatrinKlethiLezalitMarnidMatheldNizar34.JeremusKatrinKlethiLezalitMarnidNizarRolf35.JeremusKatrinKlethiMarnidNizarRolfYmira36.KatrinKlethiLezalitMarnidMatheldNizarRolf
6 Companions Party (Maximum Strictly Stable)
1.AlayenArtimennerBorchaBundukKatrinMatheld2.AlayenArtimennerBorchaBundukKatrinYmira3.AlayenArtimennerBorchaKatrinRolfYmira4.AlayenArtimennerBundukDeshaviKatrinMatheld5.AlayenArtimennerBundukDeshaviKatrinYmira6.AlayenArtimennerDeshaviKatrinLezalitMatheld7.AlayenBorchaBundukJeremusKatrinYmira8.AlayenBorchaJeremusKatrinLezalitRolf9.AlayenBorchaJeremusKatrinRolfYmira10.AlayenBundukDeshaviKatrinKlethiMatheld11.AlayenDeshaviJeremusKatrinKlethiLezalit12.AlayenDeshaviKatrinKlethiLezalitMatheld13.AlayenJeremusKatrinKlethiLezalitRolf14.AlayenJeremusKatrinKlethiRolfYmira15.AlayenKatrinKlethiLezalitMatheldRolf16.ArtimennerBaheshturBorchaBundukMatheldNizar17.ArtimennerBaheshturBorchaBundukNizarYmira18.ArtimennerBaheshturBorchaNizarRolfYmira19.ArtimennerBaheshturBundukDeshaviMatheldNizar20.ArtimennerBaheshturBundukDeshaviNizarYmira21.ArtimennerBaheshturDeshaviLezalitMatheldNizar22.ArtimennerBorchaBundukFirentisMarnidMatheld23.ArtimennerBorchaBundukFirentisMarnidYmira24.ArtimennerBorchaFirentisMarnidRolfYmira25.ArtimennerBundukDeshaviFirentisMarnidMatheld26.ArtimennerBundukDeshaviFirentisMarnidYmira27.ArtimennerDeshaviFirentisLezalitMarnidMatheld28.BaheshturBorchaBundukJeremusNizarYmira29.BaheshturBorchaJeremusLezalitNizarRolf30.BaheshturBorchaJeremusNizarRolfYmira31.BaheshturBundukDeshaviKlethiMatheldNizar32.BaheshturDeshaviJeremusKlethiLezalitNizar33.BaheshturDeshaviKlethiLezalitMatheldNizar34.BaheshturJeremusKlethiLezalitNizarRolf35.BaheshturJeremusKlethiNizarRolfYmira36.BaheshturKlethiLezalitMatheldNizarRolf37.BorchaBundukFirentisJeremusMarnidYmira38.BorchaFirentisJeremusLezalitMarnidRolf39.BorchaFirentisJeremusMarnidRolfYmira40.BundukDeshaviFirentisKlethiMarnidMatheld41.DeshaviFirentisJeremusKlethiLezalitMarnid42.DeshaviFirentisKlethiLezalitMarnidMatheld43.FirentisJeremusKlethiLezalitMarnidRolf44.FirentisJeremusKlethiMarnidRolfYmira45.FirentisKlethiLezalitMarnidMatheldRolf
Raiding Party (Maximum Strictly Stable)
1.AlayenArtimennerBorchaKatrinLezalitMatheldRolf2.ArtimennerBaheshturBorchaLezalitMatheldNizarRolf
1.AlayenArtimennerDeshaviKatrinLezalitMatheld2.AlayenDeshaviKatrinKlethiLezalitMatheld3.AlayenKatrinKlethiLezalitMatheldRolf4.ArtimennerBaheshturDeshaviLezalitMatheldNizar5.BaheshturDeshaviKlethiLezalitMatheldNizar6.BaheshturKlethiLezalitMatheldNizarRolf
Reference
Mount and Blade Wiki (Heroes): https://mountandblade.fandom.com/wiki/Heroes
Mount and Blade Wiki (Hero tactics): https://mountandblade.fandom.com/wiki/Hero_tactics
Stable party definitions: https://forums.taleworlds.com/index.php/topic,179510.0.html
Sage code: https://sagecell.sagemath.org/?z=eJx1VMFO4zAQvecrLDg4UbMR5YIUbQ6gimqX3VUFXFZVFJlm2gwkTmW7UFjx7zuOk6YJ0EPl2G_evDcz9lrVFdNiA9FGiW2hI5Q5bIH-pMk0GM2w2tbKsB_9_h1te6dyu9LMFMKwvJbcsBKfgKn64QHlJvZuWcKW_Gon890TD_k1KgpETcufoKDa2dVvoSTmtPhboRI89U5z1A1NoyX2ZkTyj1-W4hUkj5d9wB98E4qnoccOP36pDFYgJSgL7bPclGAKHIGvRAG6MLsGeyOMQtkLGkFrtSqExc0oRDzjl5zOLAF_wZso0RDwti7XI1jHQriW-lPYoWKEc3bDTugQ2Dkl3FEJrBlTQDl201IQ-KglfTVGYGfzWOlRiiG280xg186wK8gQ19bYqnV9_Tp95-CIsjM7BLr6DD217ENgU-dBJz_V6LI1A-cUhAd76bvn5bBm2ZbKaPx9EDeBOa7srL43H-taMWQo2T4-sGKk6Rb5Qb-xZiVIHwMma2PBRBEfiWg4lw6S2suE6eEUSg1fYiOxtfeUlg1CgaZomxxyn2ARGqi0HxxOIwXPoDS02g7i6ajP4dzyO3yDmPGJNsrH5VkaTDi7r40ou81Gw3KaBkHvVFL-6eHL8j9a_lZSgx6aWVjBRCYDNmE8Ynxw-lJgCU3tFgH7njSrUWoKmw4pO1p-xulwMTizip6sosfPYiYJHZKMcCTDVWSxjL-dp8HgRNqYaTMllUDpt-7mlH6Gc_uy-TMXMY-2ZW18mtR6ZxKuLeeGh9QOA_tsVZe1Sjj5NcBDehpNctadaWoEfeVYJech5Bvo0CVuCrNR8MrDNW4a2PIivEiDSBf1S9vjCu1MjF5030mbByHJ3mMlyuRe7cBFnDq7tsYlCfGJoWsxPfl2PNPh9BCgr6a9G5br4xDcDktOl6LZxo-dsBzXggb_-Aat2BBIWkbj395Tq9fr28aVwJxqzbZCmdeYD7BEEnhEnmVSVJBlLEnYSZbZXmbZiUvoGvsfmVj4ZA==&lang=sage&interacts=eJyLjgUAARUAuQ==
Source: https://steamcommunity.com/sharedfiles/filedetails/?id=1658592787
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