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of 263
pro vyhledávání: '"Graham, Ron"'
In simple card games, cards are dealt one at a time and the player guesses each card sequentially. We study problems where feedback (e.g. correct/incorrect) is given after each guess. For decks with repeated values (as in blackjack where suits do not
Externí odkaz:
http://arxiv.org/abs/2012.04019
Publikováno v:
Combinator. Probab. Comp. 31 (2022) 1-20
Consider the following experiment: a deck with $m$ copies of $n$ different card types is randomly shuffled, and a guesser attempts to guess the cards sequentially as they are drawn. Each time a guess is made, some amount of "feedback" is given. For e
Externí odkaz:
http://arxiv.org/abs/2010.05059
For a positive integer $n$, we study the number of steps to reach $n$ by a {\it Fibonacci walk} for some starting pair $a_1$ and $a_2$ satisfying the recurrence of $a_{k+2}=a_{k+1}+a_k$. The problem of slow Fibonacci walks, first suggested by Richard
Externí odkaz:
http://arxiv.org/abs/1903.08274
Publikováno v:
In Advances in Applied Mathematics May 2021 126
Juggling patterns can be described by a sequence of cards which keep track of the relative order of the balls at each step. This interpretation has many algebraic and combinatorial properties, with connections to Stirling numbers, Dyck paths, Narayan
Externí odkaz:
http://arxiv.org/abs/1504.01426
It follows from work of Chung and Graham that for a certain family of polynomials $T_{n}(x)$, derived from the descent statistic on permutations, the coefficient sequence of $T_{n-1}(x)$ coincides with that of the polynomial $T_{n}(x)/\left(1+x+\cdot
Externí odkaz:
http://arxiv.org/abs/1504.01089
We consider the following "partition and sum" operation on a natural number: Treating the number as a long string of digits insert several plus signs in between some of the digits and carry out the indicated sum. This results in a smaller number and
Externí odkaz:
http://arxiv.org/abs/1501.04067
We consider new types of perfect shuffles wherein a deck is split in half, one half of the deck is "reversed", and then the cards are interlaced. Flip shuffles are when the reversal comes from flipping the half over so that we also need to account fo
Externí odkaz:
http://arxiv.org/abs/1412.8533