Pablo Blanco, Rutgers University

Aurora Hiveley, Rutgers University

Abstract

Pablo Blanco's talk information:

Title: Generating functions of sequences relating to spanning trees in certain graph families

Generating functions of sequences relating to spanning trees in certain graph families Abstract: Kirchhoff's Matrix Tree Theorem allows us to compute the number of spanning trees of a graph by looking at its Laplacian matrix. For certain graph families (in our case, powers of cycles and paths), which are represented by finitely many states, we know by the Transfer Matrix Method that a rational generating function exists for sequences arising from structures in the family. Such a generating function can be found by computing sufficiently many terms of the sequence. In joint work with Doron Zeilberger, we found generating functions for the number of spanning trees and for a leaf-parameter by experimental methods.

Aurora Hively's talk information:

Title: Experimenting with Permutation Wordle

Consider a game of permutation wordle in which a player attempts to guess a secret permutation in Sn in as few guesses as possible. In each round, the guessing player is told which indices of their guessed permutation are correct. How can we optimize the player's strategy? Samuel Kutin and Lawren Smithline propose a strategy called cyclic shift in which all incorrect entries are shifted one index to the right in successive guesses, and they conjecture its optimality. We investigate this conjecture by formalizing what a "strategy" looks like, performing experimental analysis on inductively constructed strategies, and taking advantage of Kutin-Smithline's findings related to Eulerian numbers.

Presented Via Zoom: https://rutgers.zoom.us/j/91865817691

Password: 6564120420

For further information see: https://sites.math.rutgers.edu/~zeilberg/expmath/