Monday, November 24th, 2014

Distinguished Visiting Professor Talk Series: Sergi Elizalde, Dartmouth College, November 24th @4pm in Olin 372

Title: Consecutive patterns in permutations   Abstract: An occurrence of a consecutive pattern sigma in a permutation pi is a subsequence of adjacent entries of pi in the same relative order as the entries of sigma. For example, occurrences of the consecutive pattern 21 are descents, and alternating permutations are those that avoid the consecutive patterns 123 and 321. The systematic study of consecutive patterns in permutations started over a decade ago.  More recently, consecutive patterns have become relevant in the study of one-dimensional dynamical systems, and they are useful in creating tests to distinguish random from deterministic time series. We […]

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Tuesday, November 18th, 2014

Student Talk Series: Sergi Elizalde, Dartmouth College, November 20th, Olin 268 @ noon

Title: Lattice paths between two boundaries Abstract: Dyck paths are lattice paths with steps N=(0,1) and E=(0,1) starting at (0,0), ending at (n,n), and never going below the diagonal y=x. Among the many interesting facts known about Dyck paths, one is that the parameters ‘number of E steps at the end’ and ‘number of returns to the diagonal’ have a symmetric joint distribution, meaning that to each Dyck path we can bijectively associate another one where these parameters are interchanged. I will show that this symmetry property applies not only to Dyck paths, but more generally to lattice paths with N […]

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