Largest Stable Companion Parties

Companion combinations (Native)

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 or collection of people that not in the party, if we add him/her or them 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.	Alayen	Artimenner	Baheshtur	Borcha	Firentis	Lezalit	Matheld	Rolf
2.	Alayen	Baheshtur	Bunduk	Deshavi	Firentis	Jeremus	Klethi	Ymira
3.	Artimenner	Borcha	Katrin	Lezalit	Marnid	Matheld	Nizar	Rolf
4.	Bunduk	Deshavi	Jeremus	Katrin	Klethi	Marnid	Nizar	Ymira

7 companions party (Maximum strictly stable)

1.	Alayen	Artimenner	Baheshtur	Borcha	Bunduk	Firentis	Matheld
2.	Alayen	Artimenner	Baheshtur	Borcha	Bunduk	Firentis	Ymira
3.	Alayen	Artimenner	Baheshtur	Borcha	Firentis	Rolf	Ymira
4.	Alayen	Artimenner	Baheshtur	Bunduk	Deshavi	Firentis	Matheld
5.	Alayen	Artimenner	Baheshtur	Bunduk	Deshavi	Firentis	Ymira
6.	Alayen	Artimenner	Baheshtur	Deshavi	Firentis	Lezalit	Matheld
7.	Alayen	Artimenner	Borcha	Katrin	Lezalit	Matheld	Rolf
8.	Alayen	Baheshtur	Borcha	Bunduk	Firentis	Jeremus	Ymira
9.	Alayen	Baheshtur	Borcha	Firentis	Jeremus	Lezalit	Rolf
10.	Alayen	Baheshtur	Borcha	Firentis	Jeremus	Rolf	Ymira
11.	Alayen	Baheshtur	Bunduk	Deshavi	Firentis	Klethi	Matheld
12.	Alayen	Baheshtur	Deshavi	Firentis	Jeremus	Klethi	Lezalit
13.	Alayen	Baheshtur	Deshavi	Firentis	Klethi	Lezalit	Matheld
14.	Alayen	Baheshtur	Firentis	Jeremus	Klethi	Lezalit	Rolf
15.	Alayen	Baheshtur	Firentis	Jeremus	Klethi	Rolf	Ymira
16.	Alayen	Baheshtur	Firentis	Klethi	Lezalit	Matheld	Rolf
17.	Alayen	Bunduk	Deshavi	Jeremus	Katrin	Klethi	Ymira
18.	Artimenner	Baheshtur	Borcha	Lezalit	Matheld	Nizar	Rolf
19.	Artimenner	Borcha	Bunduk	Katrin	Marnid	Matheld	Nizar
20.	Artimenner	Borcha	Bunduk	Katrin	Marnid	Nizar	Ymira
21.	Artimenner	Borcha	Firentis	Lezalit	Marnid	Matheld	Rolf
22.	Artimenner	Borcha	Katrin	Marnid	Nizar	Rolf	Ymira
23.	Artimenner	Bunduk	Deshavi	Katrin	Marnid	Matheld	Nizar
24.	Artimenner	Bunduk	Deshavi	Katrin	Marnid	Nizar	Ymira
25.	Artimenner	Deshavi	Katrin	Lezalit	Marnid	Matheld	Nizar
26.	Baheshtur	Bunduk	Deshavi	Jeremus	Klethi	Nizar	Ymira
27.	Borcha	Bunduk	Jeremus	Katrin	Marnid	Nizar	Ymira
28.	Borcha	Jeremus	Katrin	Lezalit	Marnid	Nizar	Rolf
29.	Borcha	Jeremus	Katrin	Marnid	Nizar	Rolf	Ymira
30.	Bunduk	Deshavi	Firentis	Jeremus	Klethi	Marnid	Ymira
31.	Bunduk	Deshavi	Katrin	Klethi	Marnid	Matheld	Nizar
32.	Deshavi	Jeremus	Katrin	Klethi	Lezalit	Marnid	Nizar
33.	Deshavi	Katrin	Klethi	Lezalit	Marnid	Matheld	Nizar
34.	Jeremus	Katrin	Klethi	Lezalit	Marnid	Nizar	Rolf
35.	Jeremus	Katrin	Klethi	Marnid	Nizar	Rolf	Ymira
36.	Katrin	Klethi	Lezalit	Marnid	Matheld	Nizar	Rolf

6 companions party (Maximum strictly stable)

1.	Alayen	Artimenner	Borcha	Bunduk	Katrin	Matheld
2.	Alayen	Artimenner	Borcha	Bunduk	Katrin	Ymira
3.	Alayen	Artimenner	Borcha	Katrin	Rolf	Ymira
4.	Alayen	Artimenner	Bunduk	Deshavi	Katrin	Matheld
5.	Alayen	Artimenner	Bunduk	Deshavi	Katrin	Ymira
6.	Alayen	Artimenner	Deshavi	Katrin	Lezalit	Matheld
7.	Alayen	Borcha	Bunduk	Jeremus	Katrin	Ymira
8.	Alayen	Borcha	Jeremus	Katrin	Lezalit	Rolf
9.	Alayen	Borcha	Jeremus	Katrin	Rolf	Ymira
10.	Alayen	Bunduk	Deshavi	Katrin	Klethi	Matheld
11.	Alayen	Deshavi	Jeremus	Katrin	Klethi	Lezalit
12.	Alayen	Deshavi	Katrin	Klethi	Lezalit	Matheld
13.	Alayen	Jeremus	Katrin	Klethi	Lezalit	Rolf
14.	Alayen	Jeremus	Katrin	Klethi	Rolf	Ymira
15.	Alayen	Katrin	Klethi	Lezalit	Matheld	Rolf
16.	Artimenner	Baheshtur	Borcha	Bunduk	Matheld	Nizar
17.	Artimenner	Baheshtur	Borcha	Bunduk	Nizar	Ymira
18.	Artimenner	Baheshtur	Borcha	Nizar	Rolf	Ymira
19.	Artimenner	Baheshtur	Bunduk	Deshavi	Matheld	Nizar
20.	Artimenner	Baheshtur	Bunduk	Deshavi	Nizar	Ymira
21.	Artimenner	Baheshtur	Deshavi	Lezalit	Matheld	Nizar
22.	Artimenner	Borcha	Bunduk	Firentis	Marnid	Matheld
23.	Artimenner	Borcha	Bunduk	Firentis	Marnid	Ymira
24.	Artimenner	Borcha	Firentis	Marnid	Rolf	Ymira
25.	Artimenner	Bunduk	Deshavi	Firentis	Marnid	Matheld
26.	Artimenner	Bunduk	Deshavi	Firentis	Marnid	Ymira
27.	Artimenner	Deshavi	Firentis	Lezalit	Marnid	Matheld
28.	Baheshtur	Borcha	Bunduk	Jeremus	Nizar	Ymira
29.	Baheshtur	Borcha	Jeremus	Lezalit	Nizar	Rolf
30.	Baheshtur	Borcha	Jeremus	Nizar	Rolf	Ymira
31.	Baheshtur	Bunduk	Deshavi	Klethi	Matheld	Nizar
32.	Baheshtur	Deshavi	Jeremus	Klethi	Lezalit	Nizar
33.	Baheshtur	Deshavi	Klethi	Lezalit	Matheld	Nizar
34.	Baheshtur	Jeremus	Klethi	Lezalit	Nizar	Rolf
35.	Baheshtur	Jeremus	Klethi	Nizar	Rolf	Ymira
36.	Baheshtur	Klethi	Lezalit	Matheld	Nizar	Rolf
37.	Borcha	Bunduk	Firentis	Jeremus	Marnid	Ymira
38.	Borcha	Firentis	Jeremus	Lezalit	Marnid	Rolf
39.	Borcha	Firentis	Jeremus	Marnid	Rolf	Ymira
40.	Bunduk	Deshavi	Firentis	Klethi	Marnid	Matheld
41.	Deshavi	Firentis	Jeremus	Klethi	Lezalit	Marnid
42.	Deshavi	Firentis	Klethi	Lezalit	Marnid	Matheld
43.	Firentis	Jeremus	Klethi	Lezalit	Marnid	Rolf
44.	Firentis	Jeremus	Klethi	Marnid	Rolf	Ymira
45.	Firentis	Klethi	Lezalit	Marnid	Matheld	Rolf

Raiding party (Maximum strictly stable)

1.	Alayen	Artimenner	Borcha	Katrin	Lezalit	Matheld	Rolf
2.	Artimenner	Baheshtur	Borcha	Lezalit	Matheld	Nizar	Rolf

1.	Alayen	Artimenner	Deshavi	Katrin	Lezalit	Matheld
2.	Alayen	Deshavi	Katrin	Klethi	Lezalit	Matheld
3.	Alayen	Katrin	Klethi	Lezalit	Matheld	Rolf
4.	Artimenner	Baheshtur	Deshavi	Lezalit	Matheld	Nizar
5.	Baheshtur	Deshavi	Klethi	Lezalit	Matheld	Nizar
6.	Baheshtur	Klethi	Lezalit	Matheld	Nizar	Rolf

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==

[grandemaizo]

А не проще скрипты поправить в Module_scripts.py? For every follover delete 2 strings - Кондратийлэйшнс, all 16 in your gang!

[Nerovar]

great job!

[Superpie]

Can we give him a hand for putting his references at the bottom of the page? How scholarly!

[magnificent microwave casserole]

You answered a question I never knew I had, but dear god I needed this answer thanks much.

[Kupu Kupu]

Good Job!

[pfroddam]

Ok, much better. Thanks. :)

[tbailey264]

oh yeah 100%. the 1's and 0's were completely making my head spin. The links to the wiki are crazy useful too, I've been using them a lot since finding this guide lol

[Manx]

Just fixed the formatting, hope it's easier to read now @pfroddam @tbailey264

[pfroddam]

Ok, i think i kind of get what you are getting at with this, but it is useless to most of us in this format. Please explain what you are doing with your diagrams and binary strings. >.<

[tbailey264]

NGL the formatting of this guide is really hard to understand, but the fact that it exists with the references is helpful!