Zobrazeno 1 - 10
of 149
pro vyhledávání: '"Petersen, T. Kyle"'
Autor:
Petersen, T. Kyle, Zhuang, Yan
For any finite partially ordered set $P$, the $P$-Eulerian polynomial is the generating function for the descent number over the set of linear extensions of $P$, and is closely related to the order polynomial of $P$ arising in the theory of $P$-parti
Externí odkaz:
http://arxiv.org/abs/2403.07181
In this paper we study a variant of the Malicious Ma\^{i}tre d' problem. This problem, attributed to computer scientist Rob Pike in Peter Winkler's book "Mathematical Puzzles: A Connoisseur's Collection", involves seating diners around a circular tab
Externí odkaz:
http://arxiv.org/abs/2401.11680
In this paper we study the problem of the Malicious Maitre d', as described in Peter Winkler's book Mathematical Puzzles: A Connoisseur's Collection. This problem, attributed to computer scientist Rob Pike, involves seating diners around a circular t
Externí odkaz:
http://arxiv.org/abs/2209.11833
Autor:
Liechty, Karl, Petersen, T. Kyle
For a fixed irrational number $\alpha$ and $n\in \mathbb{N}$, we look at the shape of the sequence $(f(1),\ldots,f(n))$ after Schensted insertion, where $f(i) = \alpha i \mod 1$. Our primary result is that the boundary of the Schensted shape is appro
Externí odkaz:
http://arxiv.org/abs/2107.11515
Let $f(x) = \alpha x + \beta \mod 1$ for fixed real parameters $\alpha$ and $\beta$. For any positive integer $n$, define the S\'os permutation $\pi$ to be the lexicographically first permutation such that $0 \leq f(\pi(0)) \leq f(\pi(1)) \leq \cdots
Externí odkaz:
http://arxiv.org/abs/2007.01132
Autor:
Fulman, Jason, Petersen, T. Kyle
In this expository article, we highlight the direct connection between card shuffling and the functions known as $P$-partitions that come from algebraic combinatorics. While many (but not all) of the results we discuss are known, we give a unified tr
Externí odkaz:
http://arxiv.org/abs/2004.01659
We study the joint distribution of descents and sign for elements of the symmetric group and the hyperoctahedral group (Coxeter groups of types $A$ and $B$). For both groups, this has an application to riffle shuffling: for large decks of cards the s
Externí odkaz:
http://arxiv.org/abs/1910.04258
We generalize the well-known broken stick problem in several ways, including a discrete "brick" analogue and a sequential "pick-up sticks/bricks" version. The limit behavior of the broken brick problem gives a combinatorial proof of the broken stick
Externí odkaz:
http://arxiv.org/abs/1906.10237
We study the connection between triangulations of a type $A$ root polytope and the resonance arrangement, a hyperplane arrangement that shows up in a surprising number of contexts. Despite an elementary definition for the resonance arrangement, the n
Externí odkaz:
http://arxiv.org/abs/1903.06595
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