Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, July 18, 2017.

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Tuesday, July 18, 2017

11:00 am in 243 Altgeld Hall,Tuesday, July 18, 2017

#### Diophantine equations with binomial coefficients and perturbations of symmetric Boolean functions

###### Luis Medina (University of Puerto Rico at Rio Piedras)

Abstract: This work establishes a connection between exponential sums of perturbations of symmetric Boolean functions and Diophantine equations of the form $$\sum_{l=0}^n \binom{n}{l} x_l=0,$$ where $x_j$ belongs to some fixed bounded subset $\Gamma$ of $\mathbb{Z}$. The concepts of trivially balanced symmetric Boolean function and sporadic balanced Boolean function are extended to this type of perturbation. An observation made by Canteaut and Videau for symmetric Boolean functions of fixed degree is extended. To be specific, it is proved that, excluding the trivial cases, balanced perturbations of fixed degree do not exist when the number of variables grows. This is a joint work with Francis N. Castro and Oscar E. González