Y by Adventure10, Mango247
The Stanley-Wilf conjecture states that for any fixed permutation of , there exists a constant such that the number of permutations of that avoid is at most .
Furedi and Hajnal made another conjecture that implies the Stanley-Wilf conjecture: for every permutation matrix . CrowdMath problem 2 is to improve the bounds on for every permutation matrix .
Klazar made another conjecture about partition avoidance that implies the Stanley-Wilf conjecture. We say that a partition of contains a partition of if there exists a subpartition of that has the same relative order as . Klazar conjectured that if avoids and , where denotes a separation between parts, then there exists a constant such that the number of partitions of avoiding is at most .
http://kam.mff.cuni.cz/~klazar/cpfsp1.pdf page 4
Marcus and Tardos proved the Stanley-Wilf conjecture by proving the Furedi-Hajnal conjecture. Klazar's conjecture remains open, and was recently listed with several other conjectures in the paper below:
https://arxiv.org/pdf/1608.02279v1.pdf
If you have ideas or questions about these papers or the conjectures, please post them here. A solution to Klazar's conjecture could imply improved bounds on the constants in the Stanley-Wilf conjecture.
Furedi and Hajnal made another conjecture that implies the Stanley-Wilf conjecture: for every permutation matrix . CrowdMath problem 2 is to improve the bounds on for every permutation matrix .
Klazar made another conjecture about partition avoidance that implies the Stanley-Wilf conjecture. We say that a partition of contains a partition of if there exists a subpartition of that has the same relative order as . Klazar conjectured that if avoids and , where denotes a separation between parts, then there exists a constant such that the number of partitions of avoiding is at most .
http://kam.mff.cuni.cz/~klazar/cpfsp1.pdf page 4
Marcus and Tardos proved the Stanley-Wilf conjecture by proving the Furedi-Hajnal conjecture. Klazar's conjecture remains open, and was recently listed with several other conjectures in the paper below:
https://arxiv.org/pdf/1608.02279v1.pdf
If you have ideas or questions about these papers or the conjectures, please post them here. A solution to Klazar's conjecture could imply improved bounds on the constants in the Stanley-Wilf conjecture.