Closed valery-uga closed 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.
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.
Dear Rafael,
I am attaching
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
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.
The fix is merged. Thanks for the precise bug report. Please let me know in the future if you find new issues.
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
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: @.***>
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.
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)
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.
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