x TO 1/x MOD p

Does the map sending x to 1/x mod p behave like a random signed involution? Let L(p) be the length of the largest

increasing subsequence of {1/2 mod p, 1/3 mod p, ..., 1/(p-2) mod p}. Jon Bober investigated the distribution of

L(p) (appropriately rescaled), and compared the results to the Tracy-Widom distributions; it is known that if one

considers all permutations, as well as some subsets, the distribution of the longest increasing subsequence is given

by the Tracy-Widom distributions. This research was inspired by a problem posed by Jim Propp.

 

PAPER:       inversemod.ps     inversemod.pdf      inversemod.dvi    inversemod.latex

FIGURES:  meannew3.ps   normalized.ps   stdev3.ps   tw.ps   twandnormal.ps   twgraphs.eps   unnormal.ps

CODE:        ntlsubseq.cpp        readdata.cpp