91 citations · 520 across the 230 of their papers we have counts for
9 papers · 1 filter
A parking function analog of the Schröder numbers
Lucy Martinez, Doron Zeilberger
Pattern avoidance is a central topic in the study of permutations. Parking functions provide a natural setting in which to ask analogous questions. In this paper, we study parking…
Approximating Pi (and other constants) by Radicals in the Footsteps of Rabbi Abraham Ibn Ezra and Guru RSJ Reddy
Doron Zeilberger
Inspired by the polymath Abraham Ibn Ezra (1089-1167) who approximated π by 20/9 times the square-root of 2, and contemporary scholar, RSJ Reddy, who gave (14-sqrt(2))/4, we point…
The Distribution of Double Deficiencies in Pattern-Avoiding Permutations
Tipaluck Krityakierne, Thotsaporn Aek Thanatipanonda, Doron Zeilberger
We study the distribution of the number of double deficiencies (DD) in permutations of length n avoiding one or two patterns of length 3. Using structural decompositions of these a…
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…