Výsledky vyhledávání - "Conger, Mark"

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Autor: Conger, Mark, Howald, Jason

This paper considers the effect of riffle shuffling on decks of cards, allowing for some cards to be indistinguishable from other cards. The dual problem of dealing a game with hands, such as bridge or poker, is also considered. The Gilbert-Shannon-R

Externí odkaz: http://arxiv.org/abs/0901.1324

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Shuffling cards for blackjack, bridge, and other card games

Autor: Conger, Mark, Viswanath, D.

This paper is about the following question: How many riffle shuffles mix a deck of card for games such as blackjack and bridge? An object that comes up in answering this question is the descent polynomial associated with pairs of decks, where the dec

Externí odkaz: http://arxiv.org/abs/math/0606031

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Normal approximations for descents and inversions of permutations of multisets

Autor: Conger, Mark, Viswanath, D.

Publikováno v: Journal of Theoretical Probability, Volume 20, Issue 2, June 2007, Pages 309-325

Normal approximations for descents and inversions of permutations of the set $\{1,2,...,n\}$ are well known. A number of sequences that occur in practice, such as the human genome and other genomes, contain many repeated elements. Motivated by such e

Externí odkaz: http://arxiv.org/abs/math/0508242

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A Refinement of the Eulerian Numbers, and the Joint Distribution of $\pi(1)$ and Des($\pi$) in $S_n$

Autor: Conger, Mark

Given a permutation $\pi$ chosen uniformly from $S_n$, we explore the joint distribution of $\pi(1)$ and the number of descents in $\pi$. We obtain a formula for the number of permutations with $\des(\pi)=d$ and $\pi(1)=k$, and use it to show that if

Externí odkaz: http://arxiv.org/abs/math/0508112

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Riffle shuffles of decks with repeated cards

Autor: Conger, Mark, Viswanath, D.

Publikováno v: Annals of Probability 2006, Vol. 34, No. 2, 804-819

By a well-known result of Bayer and Diaconis, the maximum entropy model of the common riffle shuffle implies that the number of riffle shuffles necessary to mix a standard deck of 52 cards is either 7 or 11--with the former number applying when the m

Externí odkaz: http://arxiv.org/abs/math/0503233

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