Journal of Integer Sequences, Vol. 23 (2020), Article 20.3.3

Some Combinatorics of Factorial Base Representations

Tyler Ball
Clover Park High School
Lakewood, WA 98499

Joanne Beckford
University of Pennsylvania
Philadelphia, PA 19104

Paul Dalenberg
Department of Mathematics
Oregon State University
Corvallis, OR 97331

Tom Edgar
Department of Mathematics
Pacific Lutheran University
Tacoma, WA 98447

Tina Rajabi
University of Washington
Seattle, WA 98195


Every non-negative integer can be written using the factorial base representation. We explore certain combinatorial structures arising from the arithmetic of these representations. In particular, we investigate the sum-of-digits function, carry sequences, and a partial order referred to as digital dominance. Finally, we describe an analog of a classical theorem due to Kummer that relates the combinatorial objects of interest by constructing a variety of new integer sequences.

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(Concerned with sequences A034968 A055770 A227154 A230403 A331128.)

Received March 28 2019; revised version received December 29 2019; January 10 2020. Published in Journal of Integer Sequences, February 23 2020.

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