Combinatorics Seminar - Yuval Peled

November 28, 2018
Thursday, December 6, 2018 - 10:20am to 11:15am
Cockins Hall 240
Yuval Peled

Title: Enumeration and randomized constructions of hypertrees

Speaker: Yuval Peled (Courant Institute, New York University)

Abstract: Over thirty years ago, Kalai proved a beautiful d-dimensional analog of Cayley's formula for the number of n-vertex trees. Namely, he enumerated d-dimensional hypertrees weighted by the squared size of their (d-1)-dimensional homology group. This, however, does not answer the more basic problem of unweighted enumeration of d-hypertrees, which is our concern here. We analyse a random-greedy construction of d-hypertrees and show it significantly improves the previous known lower bound for their number. Second, we introduce a model of random 1-out d-dimensional complexes, and show that it has a negligible d-dimensional homology with high probability.

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