2 citations · 2 across the 13 of their papers we have counts for
10 papers · 1 filter
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…
Generalizing OOOOOOB
Alon Danai, Paul Ellis, Thotsaporn Aek Thanatipanonda
We present three versions of the classic two-pile game \textsc{one-or-one-or-one-of-both} generalized to the multi-pile context. In each case, we explore the resulting $\mathcal{P}…
Two Dimensional Subtraction -- Transfer Games
Alon Danai, Paul Ellis, Thotsaporn Aek Thanatipanonda
We generalize the results and conjectures of Tamás Lengyel, showing that the \textsc{nim}-values of a large class of two-dimensional subtraction-transfer games are periodic. These…
The Penults of Tak: Adventures in impartial, normal-play, positional games
Boris Alexeev, Paul Ellis, Michael Richter +1
For normal play, impartial games, we define penults as those positions in which every option results in an immediate win for the other player. We explore the number of tokens in pe…
The slowest coupon collector's problem
Tipaluck Krityakierne, Thotsaporn Aek Thanatipanonda
In the classical coupon collector's problem, every box of breakfast cereal contains one coupon from a collection of n distinct coupons, each equally likely to appear. The goal is t…
No-feedback Card Guessing Game: Moments and distributions under the optimal strategy
Tipaluck Krityakierne, Poohrich Siriputcharoen, Thotsaporn Aek Thanatipanonda +1
Relying on the optimal guessing strategy recently found for a no-feedback card guessing game with -time riffle shuffles, we derive an exact, closed-form formula for the expected…
No Feedback? No Worries! The art of guessing the right card
Tipaluck Krityakierne, Thotsaporn Aek Thanatipanonda
In 1998, Ciucu published "No-feedback card guessing for dovetail shuffles", an article which gives the optimal guessing strategy for cards ( even) after riffle shuffles…
The Arithmetic-Periodicity of \textsc{cut} for
Paul Ellis, Thotsaporn Aek Thanatipanonda
\textsc{cut} is a class of partition games played on a finite number of finite piles of tokens. Each version of \textsc{cut} is specified by a cut-set $\mathcal{C}\subseteq\mathbb{…
Ansatz in a Nutshell: A comprehensive step-by-step guide to polynomial, -finite, holonomic, and -finite sequences
Tipaluck Krityakierne, Thotsaporn Aek Thanatipanonda
Given a sequence 1, 1, 5, 23, 135, 925, 7285, 64755, 641075, 6993545, 83339745,..., how can we guess a formula for it? This article will quickly walk you through the concept of ans…
Game of Pure Chance with Restricted Boundary
Ho-Hon Leung, Thotsaporn "Aek'' Thanatipanonda
We consider various probabilistic games with piles for one player or two players. In each round of the game, a player randomly chooses to add or chips to his pile under the…