Staircase rook polynomials and Cayley's game of Mousetrap

  • Authors:

  • Michael Z. Spivey

  • Affiliations:

  • Department of Mathematics and Computer Science, University of Puget Sound, Tacoma, Washington 98416-1043, USA

  • Venue:
  • European Journal of Combinatorics
  • Year:
  • 2009

Quantified Score

Hi-index 0.00

Visualization

Abstract

First introduced by Arthur Cayley in the 1850's, the game of Mousetrap involves removing cards from a deck according to a certain rule. In this paper we find the rook polynomial for the number of Mousetrap decks in which at least two specified cards are removed. We also find a new expression for the rook polynomial for the number of decks in which exactly one specified card is removed and give expressions for counts of two kinds of Mousetrap decks in terms of other known combinatorial numbers.