Reversing the deck after a top-to-random shuffle gives an operator whose minimal polynomial is a product of distinct linear factors, with roots the signed knapsack numbers: for the basic reverse shuffle, the integers -n+2, 0, n, and every integer from -n+4 to n-3.
The mathematics of shuffling cards
1 Pith paper cite this work, alongside 7 external citations. Polarity classification is still indexing.
1
Pith paper citing it
7
external citations · OpenAlex
citation-role summary
background 1
citation-polarity summary
fields
math.CO 1years
2025 1verdicts
ACCEPT 1roles
background 1polarities
background 1representative citing papers
citing papers explorer
-
Top to random and reverse: analysis of a new descent algebra shuffle
Reversing the deck after a top-to-random shuffle gives an operator whose minimal polynomial is a product of distinct linear factors, with roots the signed knapsack numbers: for the basic reverse shuffle, the integers -n+2, 0, n, and every integer from -n+4 to n-3.