Varun Shah, University of Washington
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PDL C-401
Why is 7¹³¹−7 divisible by 131? How can we easily tell whether \binom{146}{k} is odd? Why is the number of such k a power of 2? In this talk, we explore how many such questions can be answered using a single tool: bijective combinatorics. By realizing these familiar expressions as sizes of sets of combinatorial objects, divisibility and parity emerge from hidden symmetries of these sets.
Since this is a pictionary talk, all proofs will be proofs in pictures.