Outline and Links for Doron Zeilberger's Talk at the Journal of Algebraic Combinatorics (JACO) webminar, July 26, 2023, 11:30 EDT

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.

IN A NUTSHELL:

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

1. Gian-Carlo Rota's charming 1994 talk

2. Dr. Z.'s Opinion 5

3. Richard Stanley's Essay

4. The New JACO (under the leadership of Ilias Kotsireas), [Lots of great articles, e.g. one by Bill Chen and Amy Fu]

5. ALCO: Algebraic Combinatorics gone astray:

6. Kauers-Z masterpiece rejected by ALCO for the Goluden-Jackson issue

7. Opinion 178 of Dr. Z.

8. Symmetric Chain Decomposition of the Boolean Lattice:

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:

Ap:=proc(L,c): [op(L),c]:end: Du1:=proc(C) local i,k:k:=nops(C):if k=1 then [[seq(Ap(C[i],0),i=1..k),Ap(C[k],1)]]: else [[seq(Ap(C[i],1),i=1..k-1)],[seq(Ap(C[i],0),i=1..k),Ap(C[k],1)]]:fi:end: SCD1:=proc(n) local S,i:option remember:if n=1 then RETURN([[[0],[1]]]): else S:=SCD1(n-1):[seq(op(Du1(S[i])),i=1..nops(S))]:fi:end:
9. (Shame on you: Patrice Ossona de Mendez, editor-in-chief of the European Journal of Combinatorics)

10. The Bottom Line (as Gian-Carlo Rota would say)

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.