New Bounties

by BlakeKeiller, Sunday, January 24, 2021, 20:54 (315 days ago)

20 new bounties from the bounty reward fund have been placed. All the propositions are again Ramsey problems, specifically dealing with the values of R(3,6), R(4,5), R(3,7), R(4,6) and R(5,5).

Six of the propositions correspond to the best known bounds of R(3,7), R(4,6) and R(5,5). A bounty of (almost) 300 bars was placed on each.

R(3,7) > 22: not_TwoRamseyProp_3_7_22 : TMJKbZjgHwR1R1hCak4EgwPjmA8HNR1AzVe
R(3,7) <= 23: TwoRamseyProp_3_7_23 : TMGKH8FtpMKQL5nSjsU22A45gjtZpd5Yarm
R(4,6) > 35: not_TwoRamseyProp_4_6_35 : TMTP6yNEuLJgxabKFMpXXG2jXMmGBhXo7LG
R(4,6) <= 41: TwoRamseyProp_4_6_41 : TMGyu8j3dnjTxE99spsMGXnkEp8QU5d7ePK
R(5,5) > 42: not_TwoRamseyProp_5_5_42 : TMbu5cNHpJ8J5t435KssbZiaKf7Av2ASGBH
R(5,5) <= 48: TwoRamseyProp_5_5_48 : TMctie53cBVHdM4Dvc2CpJMCm7QGMPDGRQm

Four of the propositions correspond to open problems. A bounty of (almost) 500 bars was placed on each.

R(4,6) > 36: TwoRamseyProp_4_6_36 : TMUnmw49fNPNqFFquQctTBy16LwoDRrxTg7
R(4,6) <= 40: TwoRamseyProp_4_6_40 : TMN4q5W37NkZMoR6vedSpCh9okznLfUoQbH
R(5,5) > 43: TwoRamseyProp_5_5_43 : TMNUq5RbcM6eMfgZZQwN7xZNjZQaoV9H2Vo
R(5,5) <= 47: TwoRamseyProp_5_5_47 : TMHQLAu8LNq833psgUYemBdTPiRj2wTeAyb

The remaining ten are weaker bounds than the best known and are stated using power sets. A bounty of (almost) 100 bars was placed on each.

R(3,6) > 16: not_TwoRamseyProp_3_6_Power_4 : TMLyvZypyq14D3Q2vyHSse88YzHewwRcCDB
R(3,7) > 16: not_TwoRamseyProp_3_7_Power_4 : TMRgsDDE1r3HdbuN5FnQLLbtL4VxT2U4oxm
R(4,5) > 16: not_TwoRamseyProp_4_5_Power_4 : TMK6infbDwDHS4b8r9xmZohrD5GBwPDg9Y6
R(4,6) > 32: not_TwoRamseyProp_4_6_Power_5 : TMNEbNDi1x9cRwNgQ365q4mQrTA21mcZzpE
R(5,5) > 32: not_TwoRamseyProp_5_5_Power_5 : TMGmDYbRXrpoiZjRi312cY1fvzjX3vVcMbz
R(3,6) <= 32: TwoRamseyProp_3_6_Power_5 : TMVhEw2QbtGaDDY51t2cwuHDMUzaETWib2D
R(3,7) <= 32: TwoRamseyProp_3_7_Power_5 : TMb4eT18NCpi4ejC4ECKxNQaagNAEGTj4LA
R(4,5) <= 32: TwoRamseyProp_4_5_Power_5 : TMV3YoyvmjyjxRvvRFvzzy1SBNJiVLAPcj7
R(4,6) <= 64: TwoRamseyProp_4_6_Power_6 : TMd3rAdqu6qzfWvG6z8fctmdsnvMEex6ykJ
R(5,5) <= 64: TwoRamseyProp_5_5_Power_6 : TMFmfYexZpQQTd5iYiCqFrsY32PBd2EqPzm