18 citations · 44 across the 8 of their papers we have counts for
7 papers · 1 filter
Boolean Function Analogs of Covering Systems
Anthony Zaleski, Doron Zeilberger
Bob Hough recently disproved a long-standing conjecture of Paul Erdős regarding covering systems. Inspired by his seminal paper, we describe analogs of covering systems to Boolean…
Experimental analysis of lattice walks
Anthony Zaleski
Feller's book An Introduction to Probability Theory and Its Application discusses statistics corresponding to sequences of coin tosses, with a dollar being won or lost depending on…
On the Intriguing Problem of Counting (n+1,n+2)-Core Partitions into Odd Parts
Anthony Zaleski, Doron Zeilberger
Tewodros Amdeberhan and Armin Straub initiated the study of enumerating subfamilies of the set of (s,t)-core partitions. While the enumeration of (n+1,n+2)-core partitions into dis…
Counting Permutations that Avoid Many Patterns
Yonah Biers-Ariel, Haripriya Chakraborty, John Chiarelli +8
This paper presents a collection of experimental results regarding permutation pattern avoidance, focusing on cases where there are "many" patterns to be avoided.
Explicit expressions for the moments of the size of an (n, dn-1)-core partition with distinct parts
Anthony Zaleski
In a previous paper (arXiv:1608.02262), we used computer-assisted methods to find explicit expressions for the moments of the size of a uniform random (n,n+1)-core partition with d…
Explicit (Polynomial!) Expressions for the Expectation, Variance and Higher Moments of the Size of a (2n + 1, 2n + 3)-core partition with Distinct Parts
Anthony Zaleski, Doron Zeilberger
Inspired by Armin Straub's conjecture (arXiv:1601.07161) about the number and maximal size of (2n+1, 2n+3)-core partitions with distinct parts, we develop relatively efficient, sym…
Explicit expressions for the moments of the size of an (s,s+1)-core partition with distinct parts
Anthony Zaleski
For fixed s, the size of an (s, s+1)-core partition with distinct parts can be seen as a random variable X_s. Using computer-assisted methods, we derive formulas for the expectatio…