Journal of Integer Sequences, Vol. 25 (2022), Article 22.6.8

Counting Tournament Brackets

John P. D'Angelo
Department of Mathematics
University of Illinois
1409 W. Green St.
Urbana, IL 61801


Motivated by a question involving tournament brackets, we study the number W(N) of N-tuples satisfying a system of natural inequalities. Our analysis yields a doubly-indexed recurrence relation evoking Pascal's formula and an interesting sequence of polynomials. We provide upper and lower bounds for W(N) (which grows faster than exponentially) and methods for computing it.

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(Concerned with sequences A028361 A355519.)

Received April 19 2022; revised versions received July 4 2022; July 5 2022. Published in Journal of Integer Sequences, July 27 2022.

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