Abstract
					We show that the longest $k$-alternating substring of a random permutation has length asymptotic to $2(n-k)/3$.
				
			
			
																																																
					
													Author Biographies
											
																		
								
																																							Igor Pak, University of California at Los Angeles
																	
								
									Department of Mathematics
								
							 
																								
								
																																							Robin Pemantle, University of Pennsylvania
																	
								
									Department of Mathematics