17 papers
Estimating Many Constants With a Coin
Shalosh B. Ekhad, Doron Zeilberger
We extend, and fully implement, in Maple, Jim Propp's charming way of estimating Pi via tossing a fair coin, and compute many other constants, even going beyond the far more genera…
The Combinatorics of Multi-Lane Merging
Aurora Hiveley, Doron Zeilberger
We extend the nice treatment of V. Bardenova, E. Insko, K. Johnson, and S. Sullivan of the combinatorics of two-lane mergings to the multi-lane case.
A quick proof that -avoiding permutations without double deficiencies are counted by the Motzkin numbers
Tipaluck Krityakierne, Thotsaporn "Aek" Thanatipanonda, Doron Zeilberger
We present a short "proof from the Book" that -avoiding permutations without double deficiencies are counted by the Motzkin numbers. Although this result was first proved by R…
In How Many Ways can a Rectangle be Rectangled?
Pablo Blanco, Robert Dougherty-Bliss, Natalya Ter-Saakov +1
There are ways to tile a rectangle with rectangular tiles (of any length, of course they all must have width ), but in how many ways can you tile a $100 \…
Counting (and Randomly Generating) Hamiltonian Cycles in Rectangular Grids
Pablo Blanco, Doron Zeilberger
We first fully implement, in Maple, the ingenious method of Robert Stoyan and Volker Strehl from 1995 to automatically derive generating functions for the number of Hamiltonian cyc…
Cutting 4 by grids into two congruent pieces
Robert Dougherty-Bliss, Natalya Ter-Saakov, Doron Zeilberger
In the March 2025 issue of Pour la Science, Jean-Paul Delahaye described a wonderful solution to the following problem: How many ways can you divide a 3 by 2n rectangle into two co…