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rgugliel / CoxIter

CoxIter is a computer program designed to compute invariants of hyperbolic Coxeter groups.
GNU General Public License v3.0
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Another false negative for finite covolume #25

Closed valery-uga closed 1 year ago

valery-uga commented 1 year ago

I am attaching an input file for a Coxeter diagram which is known to me to have finite covolume. This can be checked in two ways: (1) Directly by Vinberg's sufficient condition: there are no broken edges of Lanner subdiagrams and every parabolic subdiagram is contained in a maximal parabolic, (2) also directly, by computing the polyhedron in the Minkowski space with either sage or polymake and confirming that all rays lie inside the closure of the positive cone. The number of the vertices on the boundary is 127.

However, Coxiter says that this diagram has infinite covolume and that the number of vertices on the boundary is 130.

Valery

coxiter-infile.txt

rgugliel commented 1 year ago

Hello @valery-uga , Thanks for the precise report. I'll have a look when I have time (but please keep in mind that I am not in academics anymore and that I do that in my free time). I'll keep you updated.

Small question: did you check (1) yourself? If you have a list of all parabolic subdiagrams and their inclusion in a maximal one, that would greatly speed up the investigation.

rgugliel-da commented 1 year ago

However, Coxiter says that this diagram has infinite covolume and that the number of vertices on the boundary is 130.

Can you share CoxIter output? On my side it says "?" for the cofiniteness, which indeed indicates that something is fishy.

valery-uga commented 1 year ago

Dear Rafael,

I am attaching

  1. the Coxiter output file
  2. the 314 connected parabolic subgraphs, as a text file with vertices,
  3. the same for the 127 maximal by inclusion parabolic subgraphs; they all have maximal rank.
  4. the intersection matrix between the 24 vectors from which all these were derived.

I tried to send sagemath pickle files with the actual graphs but I guess GitHub does not support those. I hope this helps.

Best Valery

connected_parabolic_vertices.txt intersection_matrix.txt maximal_parabolic_vertices.txt out-coxiter.txt

rgugliel commented 1 year ago

Hey! Just to let you know that I narrowed down the issue to a very small example. I should be able to push a fix this week-end.

rgugliel commented 1 year ago

The fix is merged. Thanks for the precise bug report. Please let me know in the future if you find new issues.

valery-uga commented 1 year ago

Here are two more diagrams for which the previous version gave a false negative for the covolume. I am including both input and output files. in-cox16_6_1_h_20.txt in-cox18_4_0_h_14.14.txt out-cox16_6_1_h_20.txt out-cox18_4_0_h_14.14.txt

valery-uga commented 1 year ago

Just to make sure: the latest version of Coxiter says that this diagram has finite covolume, is that correct?

I have two more diagrams for which Coxiter falsely reported infinite covolume. I wonder what the new version does. Should I post them here? I can also send them privately if I knew where.

Valery

On Sat, Oct 8, 2022 at 7:02 AM Rafael Guglielmetti @.***> wrote:

The fix is merged. Thanks for the precise bug report. Please let me know in the future if you find new issues.

— Reply to this email directly, view it on GitHub https://github.com/rgugliel/CoxIter/issues/25#issuecomment-1272293367, or unsubscribe https://github.com/notifications/unsubscribe-auth/A3F6UROL3FR5AYP7PLTJ373WCFIE5ANCNFSM6AAAAAAQRNZD6I . You are receiving this because you were mentioned.Message ID: @.***>

rgugliel commented 1 year ago

Yes: the diagram for which you created the issue is now reported as cofinite. For the other two that you share, I'll test them soon and let you know.

rgugliel commented 1 year ago

Just checked your two other groups, the cofiniteness test is correct now.

First graph

Reading graph:
    Number of vertices: 118
    Dimension: 15
    Vertices: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117
    Field generated by the entries of the Gram matrix: ?
File read

Finding connected subgraphs......
Finding graphs products......
Computations......
    Computation time: 100398s

Information
    Cocompact: no
    Finite covolume: yes
    f-vector: (305053, 2769750, 10580390, 24132025, 37594380, 42639124, 36383665, 23721915, 11860435, 4516864, 1286454, 264635, 36910, 3090, 118, 1)
    Number of vertices at infinity: 8917
    Alternating sum of the components of the f-vector: 2
    Euler characteristic: 0

Growth series:
f(x) = C(2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,7,8,8,8,9,10,10,10,11,12,12,12,14,15,16,18,20,22,24,30)/(1 - 103 * x + 642 * x^2 - 1055 * x^3 + 1439 * x^4 - 5628 * x^5 + 7096 * x^6 - 9613 * x^7 + 24715 * x^8 - 27586 * x^9 + 71710 * x^10 - 85245 * x^11 + 156499 * x^12 - 266691 * x^13 + 328271 * x^14 - 686318 * x^15 + 721753 * x^16 - 1575307 * x^17 + 1650077 * x^18 - 3231725 * x^19 + 3748006 * x^20 - 6211309 * x^21 + 8150362 * x^22 - 11341444 * x^23 + 16753551 * x^24 - 20106078 * x^25 + 32427363 * x^26 - 34834500 * x^27 + 59380314 * x^28 - 59426322 * x^29 + 103268825 * x^30 - 99771826 * x^31 + 171670784 * x^32 - 164785046 * x^33 + 274032921 * x^34 - 266862445 * x^35 + 422111873 * x^36 - 423025842 * x^37 + 629566082 * x^38 - 655215506 * x^39 + 912484004 * x^40 - 990879538 * x^41 + 1288313301 * x^42 - 1462497507 * x^43 + 1776524120 * x^44 - 2107281578 * x^45 + 2396743680 * x^46 - 2965377874 * x^47 + 3169438557 * x^48 - 4078088535 * x^49 + 4113269567 * x^50 - 5484834200 * x^51 + 5246039886 * x^52 - 7219841237 * x^53 + 6580833582 * x^54 - 9308363543 * x^55 + 8127605230 * x^56 - 11762726337 * x^57 + 9888362713 * x^58 - 14578693738 * x^59 + 11859580946 * x^60 - 17731923170 * x^61 + 14026621508 * x^62 - 21176502343 * x^63 + 16367526622 * x^64 - 24842950306 * x^65 + 18846894338 * x^66 - 28639984777 * x^67 + 21421772827 * x^68 - 32455226613 * x^69 + 24035454757 * x^70 - 36160962001 * x^71 + 26625592169 * x^72 - 39617329618 * x^73 + 29118244443 * x^74 - 42681723778 * x^75 + 31438633776 * x^76 - 45213259308 * x^77 + 33505205141 * x^78 - 47084416912 * x^79 + 35242593235 * x^80 - 48184990451 * x^81 + 36575307392 * x^82 - 48433639288 * x^83 + 37442212959 * x^84 - 47778784279 * x^85 + 37789168293 * x^86 - 46208314015 * x^87 + 37583762625 * x^88 - 43745708711 * x^89 + 36806021394 * x^90 - 40456150927 * x^91 + 35462464413 * x^92 - 36437100771 * x^93 + 33574213174 * x^94 - 31820868109 * x^95 + 31189433497 * x^96 - 26760260655 * x^97 + 28368717321 * x^98 - 21428582750 * x^99 + 25195701376 * x^100 - 16002097633 * x^101 + 21760248111 * x^102 - 10659589771 * x^103 + 18167440703 * x^104 - 5564284702 * x^105 + 14519534563 * x^106 - 865266739 * x^107 + 10924214364 * x^108 + 3318835415 * x^109 + 7476883169 * x^110 + 6894781478 * x^111 + 4268911865 * x^112 + 9807246565 * x^113 + 1371520334 * x^114 + 12029435399 * x^115 - 1154931978 * x^116 + 13571596598 * x^117 - 3274357283 * x^118 + 14467673749 * x^119 - 4964406238 * x^120 + 14780328338 * x^121 - 6226793494 * x^122 + 14585424693 * x^123 - 7075572021 * x^124 + 13975318473 * x^125 - 7544429591 * x^126 + 13043122818 * x^127 - 7674581091 * x^128 + 11885813464 * x^129 - 7519901967 * x^130 + 10590398781 * x^131 - 7135389781 * x^132 + 9238307584 * x^133 - 6580896048 * x^134 + 7894576760 * x^135 - 5911191498 * x^136 + 6613916272 * x^137 - 5179485235 * x^138 + 5433101879 * x^139 - 4429651133 * x^140 + 4378527141 * x^141 - 3699863936 * x^142 + 3461358883 * x^143 - 3017500233 * x^144 + 2685411493 * x^145 - 2403069678 * x^146 + 2043877009 * x^147 - 1867354401 * x^148 + 1526810734 * x^149 - 1415417731 * x^150 + 1118689959 * x^151 - 1045288986 * x^152 + 804367093 * x^153 - 751657524 * x^154 + 566866146 * x^155 - 525554143 * x^156 + 391744134 * x^157 - 357096128 * x^158 + 264835675 * x^159 - 235396040 * x^160 + 175224036 * x^161 - 150515099 * x^162 + 112980163 * x^163 - 93240609 * x^164 + 70994416 * x^165 - 56017634 * x^166 + 43151276 * x^167 - 32627784 * x^168 + 25416278 * x^169 - 18457084 * x^170 + 14329341 * x^171 - 10128849 * x^172 + 7785401 * x^173 - 5405633 * x^174 + 3997488 * x^175 - 2793310 * x^176 + 1986685 * x^177 - 1380848 * x^178 + 921808 * x^179 - 645597 * x^180 + 431169 * x^181 - 277587 * x^182 + 173509 * x^183 - 114931 * x^184 + 70749 * x^185 - 43470 * x^186 + 20975 * x^187 - 15086 * x^188 + 8916 * x^189)

Second graph


Reading graph:
    Number of vertices: 48
    Dimension: 17
    Vertices: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47
    Field generated by the entries of the Gram matrix: Q[sqrt(2)]
File read

Finding connected subgraphs......
Finding graphs products......
Computations......
    Computation time: 92858.5s

Information
    Cocompact: no
    Finite covolume: yes
    f-vector: (196052, 1941741, 8423168, 22443484, 41829856, 58083240, 62162888, 52211444, 34678368, 18206371, 7499104, 2388668, 575560, 101658, 12584, 1020, 48, 1)
    Number of vertices at infinity: 5244
    Alternating sum of the components of the f-vector: 2
    Euler characteristic: 0

Growth series:
f(x) = C(2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,7,7,8,8,8,8,9,9,10,10,10,11,12,12,12,12,13,14,14,15,16,16,18,18,20,22,24,26,28,30,32)/(1 - 31 * x + 180 * x^2 - 172 * x^3 - 197 * x^4 - 677 * x^5 + 1063 * x^6 - 1489 * x^7 + 5017 * x^8 - 6415 * x^9 + 18388 * x^10 - 18620 * x^11 + 41268 * x^12 - 65660 * x^13 + 100003 * x^14 - 177813 * x^15 + 217816 * x^16 - 443592 * x^17 + 499842 * x^18 - 985430 * x^19 + 1140550 * x^20 - 2066746 * x^21 + 2572097 * x^22 - 4073655 * x^23 + 5602490 * x^24 - 7831358 * x^25 + 11719769 * x^26 - 14663423 * x^27 + 23403932 * x^28 - 27155124 * x^29 + 44785486 * x^30 - 49733242 * x^31 + 82387183 * x^32 - 90257489 * x^33 + 146219821 * x^34 - 161616715 * x^35 + 251534468 * x^36 - 285210228 * x^37 + 421004376 * x^38 - 494181208 * x^39 + 687991864 * x^40 - 839564728 * x^41 + 1101003878 * x^42 - 1396628418 * x^43 + 1730235984 * x^44 - 2274297768 * x^45 + 2675042121 * x^46 - 3625058191 * x^47 + 4076307829 * x^48 - 5659104491 * x^49 + 6129153312 * x^50 - 8657472080 * x^51 + 9102256458 * x^52 - 12990065950 * x^53 + 13358092972 * x^54 - 19132855588 * x^55 + 19381633829 * x^56 - 27687127515 * x^57 + 27806241049 * x^58 - 39397872903 * x^59 + 39453021847 * x^60 - 55173479849 * x^61 + 55360532289 * x^62 - 76100201831 * x^63 + 76828610898 * x^64 - 103456170902 * x^65 + 105446709114 * x^66 - 138720787454 * x^67 + 143136162219 * x^68 - 183574497309 * x^69 + 192160869107 * x^70 - 239896154173 * x^71 + 255159028194 * x^72 - 309746858110 * x^73 + 335121892630 * x^74 - 395346973146 * x^75 + 435394714070 * x^76 - 499035958338 * x^77 + 559609992159 * x^78 - 623232741049 * x^79 + 711646489882 * x^80 - 770362755382 * x^81 + 895494468091 * x^82 - 942799181397 * x^83 + 1115171226020 * x^84 - 1142765556428 * x^85 + 1374514787953 * x^86 - 1372256043543 * x^87 + 1677050424278 * x^88 - 1632914347786 * x^89 + 2025727561532 * x^90 - 1925954038068 * x^91 + 2422760915823 * x^92 - 2252014305297 * x^93 + 2869322164148 * x^94 - 2611091828828 * x^95 + 3365402050355 * x^96 - 3002400390477 * x^97 + 3909500161674 * x^98 - 3424323021358 * x^99 + 4498543245254 * x^100 - 3874288117258 * x^101 + 5127633957735 * x^102 - 4348779573657 * x^103 + 5790084231045 * x^104 - 4843233455355 * x^105 + 6477253827761 * x^106 - 5352122465839 * x^107 + 7178760609996 * x^108 - 5868906486380 * x^109 + 7882447796930 * x^110 - 6386191517166 * x^111 + 8574777592534 * x^112 - 6895737711250 * x^113 + 9240953232371 * x^114 - 7388721376093 * x^115 + 9865495559630 * x^116 - 7855780345522 * x^117 + 10432472426075 * x^118 - 8287370183709 * x^119 + 10926236806138 * x^120 - 8673856777878 * x^121 + 11331708713712 * x^122 - 9005927824544 * x^123 + 11635176281847 * x^124 - 9274702424705 * x^125 + 11824567042184 * x^126 - 9472193525568 * x^127 + 11890221126991 * x^128 - 9591374637201 * x^129 + 11825029243358 * x^130 - 9626650511170 * x^131 + 11625106229261 * x^132 - 9573867427331 * x^133 + 11289712680695 * x^134 - 9430724144073 * x^135 + 10821722304157 * x^136 - 9196683684867 * x^137 + 10227298020490 * x^138 - 8873316050254 * x^139 + 9516114467832 * x^140 - 8464054501392 * x^141 + 8700747263105 * x^142 - 7974442848943 * x^143 + 7796685044798 * x^144 - 7411753759098 * x^145 + 6821471790161 * x^146 - 6785104657151 * x^147 + 5794531468820 * x^148 - 6104945991732 * x^149 + 4736174961500 * x^150 - 5383090364492 * x^151 + 3667326835251 * x^152 - 4632071692397 * x^153 + 2608476767753 * x^154 - 3865121463607 * x^155 + 1579444610093 * x^156 - 3095477790235 * x^157 + 598391213942 * x^158 - 2336326128882 * x^159 - 318308509455 * x^160 - 1600118518631 * x^161 - 1156866695956 * x^162 - 898560232092 * x^163 - 1906030497607 * x^164 - 241968014351 * x^165 - 2557661384812 * x^166 + 360648728268 * x^167 - 3106443236104 * x^168 + 902114585040 * x^169 - 3550224608023 * x^170 + 1376910553809 * x^171 - 3889527744076 * x^172 + 1781553815324 * x^173 - 4127651721453 * x^174 + 2114287946699 * x^175 - 4270038282546 * x^176 + 2375338383390 * x^177 - 4324220910002 * x^178 + 2566480616846 * x^179 - 4299097167930 * x^180 + 2691164939318 * x^181 - 4204804793215 * x^182 + 2754022525377 * x^183 - 4052006978607 * x^184 + 2760890585225 * x^185 - 3851746316655 * x^186 + 2718281036609 * x^187 - 3614819735088 * x^188 + 2633374675864 * x^189 - 3351690868094 * x^190 + 2513497492026 * x^191 - 3071981385663 * x^192 + 2366108517073 * x^193 - 2784480690344 * x^194 + 2198348743328 * x^195 - 2496792157843 * x^196 + 2017053118613 * x^197 - 2215427208864 * x^198 + 1828385277848 * x^199 - 1945604613544 * x^200 + 1637913003920 * x^201 - 1691428385921 * x^202 + 1450337158751 * x^203 - 1455795603006 * x^204 + 1269620966098 * x^205 - 1240632352057 * x^206 + 1098825596375 * x^207 - 1046885710202 * x^208 + 940279222150 * x^209 - 874767558107 * x^210 + 795490985949 * x^211 - 723796414772 * x^212 + 665354668204 * x^213 - 593028399062 * x^214 + 550113331778 * x^215 - 481104709676 * x^216 + 449565739740 * x^217 - 386451096579 * x^218 + 363068121733 * x^219 - 307317744663 * x^220 + 289719796721 * x^221 - 241926365192 * x^222 + 228373594840 * x^223 - 188495015898 * x^224 + 177795275230 * x^225 - 145338380055 * x^226 + 136665525809 * x^227 - 110867946047 * x^228 + 103700927969 * x^229 - 83654349335 * x^230 + 77647564865 * x^231 - 62411986531 * x^232 + 57361675725 * x^233 - 46027244046 * x^234 + 41790185810 * x^235 - 33535952638 * x^236 + 30021936282 * x^237 - 24131576120 * x^238 + 21257097192 * x^239 - 17137414387 * x^240 + 14834086037 * x^241 - 12005094631 * x^242 + 10197036121 * x^243 - 8288616316 * x^244 + 6905798588 * x^245 - 5636494086 * x^246 + 4604361890 * x^247 - 3771294014 * x^248 + 3023692514 * x^249 - 2481017718 * x^250 + 1953782426 * x^251 - 1602782934 * x^252 + 1243081242 * x^253 - 1016048915 * x^254 + 777478917 * x^255 - 631266951 * x^256 + 478630689 * x^257 - 384129264 * x^258 + 289055600 * x^259 - 228652452 * x^260 + 171653916 * x^261 - 133129133 * x^262 + 99639395 * x^263 - 75726402 * x^264 + 56758870 * x^265 - 42080869 * x^266 + 31393683 * x^267 - 22846614 * x^268 + 17025178 * x^269 - 12098096 * x^270 + 8858672 * x^271 - 6246876 * x^272 + 4535740 * x^273 - 3134445 * x^274 + 2189011 * x^275 - 1529644 * x^276 + 1053612 * x^277 - 709946 * x^278 + 457718 * x^279 - 321993 * x^280 + 213535 * x^281 - 132031 * x^282 + 77553 * x^283 - 53801 * x^284 + 34727 * x^285 - 17320 * x^286 + 8344 * x^287 - 6677 * x^288 + 5243 * x^289)
valery-uga commented 1 year ago

Great. I confirm that I got the same numbers of vertices at infinity: 8917 and 5244 respectively. These are the diagrams (16,6,1) and (18,4,0) in https://arxiv.org/abs/2209.09110.