Title: What is Algebraic Combinatorics and What Should It Be
Abstract: I will survey the history and trends of this relatively new field, and speculate about the future, and discuss what it SHOULD be, but also what it should NOT be.
What is (current) Algebraic Combinatorics: Pretentious, Pompous, Snotty, Overly Abstract
What Should it Be: Inclusive, Open-Minded, and Include ALL kinds of algebra, including "high school algebra" so efficiently implemented in Computer Algebra Systems
An example of "Elementary" (but interesting!) Algebraic Combinatorics
Du:=proc(C,n) local k,i: k:=nops(C): if k=1 then {[C[1],C[1] union {n}]} else {[op(C),C[k] union {n}],[seq(C[i] union {n},i=1..k-1)]}:fi:end: SCD:=proc(n) local S,C: option remember: if n=1 then RETURN({[{},{1}]} ): else S:=SCD(n-1): {seq(op(Du(C,n)), C in S)}:fi:end:
What is (current) Algebraic Combinatorics: Pretentious, Pompous, Snotty, Overly Abstract, Elitist, Human-Centric
What Should it Be: Inclusive, Open-Minded, and Include ALL kinds of algebra, including "high school algebra" so efficiently implemented in Computer Algebra Systems
Added Aug. 7, 2023: Xiangdong Wen's masterpiece is now published in a much better journal!. See also preliminary notes to a video.
Personal Journal of Shalosh B. Ekhad and Doron Zeilberger