91 citations · 520 across the 230 of their papers we have counts for
7 papers · 2 filters
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…
Going Back to Neil Sloane's FIRST LOVE (OEIS Sequence A435): On the Total Heights in Rooted Labeled Trees
Shalosh B. Ekhad, Doron Zeilberger
In this tribute to Neil Sloane, we revisit the first sequence in the On-Line Encyclopedia of Integer Sequences, sequence A435 (1, 8, 78, 944, 13800, 237432, 4708144, 105822432, ...…
A Motivated Rendition of the Ellenberg-Gijswijt Gorgeous proof that the Largest Subset of with No Three-Term Arithmetic Progression is , with $c=\root 3 \of {(5589+891\,\sqrt {33})}/8=2.75510461302363300022127...$
Doron Zeilberger
Inspired by the Croot-Lev-Pach breakthrough, Jordan Ellenberg and Dion Gijswijt have recently amazed the combinatorial world by proving that the largest size of a subset of …
Using the "Freshman's Dream" to Prove Combinatorial Congruences
Moa Apagodu, Doron Zeilberger
In a recent beautiful but technical article, William Y.C. Chen, Qing-Hu Hou, and Doron Zeilberger developed an algorithm for finding and proving congruence identities (modulo prime…
Integrals Involving Rudin-Shapiro Polynomials and Sketch of a Proof of Saffari's Conjecture
Shalosh B. Ekhad, Doron Zeilberger
Continuing pioneering work of Christophe Doche and Laurent Habsieger from 2004, we develop computer algebra algorithms, implemented in Maple, for finding the (necessarily rational)…
On the number of Singular Vector Tuples of Hyper-Cubical Tensors
Shalosh B. Ekhad, Doron Zeilberger
Shmuel Friedland and Giorgio Ottaviani's beautiful constant term expression for the number of singular vector tuples of generic tensors is used to derive a rational generating func…
Doron Gepner's Statistics on Words in {1,2,3} is (most probably) Asymptotically Logistic
Doron Zeilberger
Doron Gepner's word statistics, that came up in his research in conformal field theory, is studied and it is conjectured that its scaled limiting distribution is the Logistic distr…