George David Birkhoff

Proof of George Andrews's and David Robbins's q-TSPP Conjecture

1 Proemium In the historical conference Combinatoire Énumerative that took place at the end of May 1985 in Montréal, Richard Stanley raised some intriguing problems about the enumeration of plane partitions (see below), which he later expanded into a fascinating article [11]. Most of these problems concerned the enumeration of “symmetry classes” of plane partitions that were discussed in more d...

A PROOF OF GEORGE ANDREWS’ AND DAVID ROBBINS’ q-TSPP CONJECTURE

The conjecture that the orbit-counting generating function for totally symmetric plane partitions can be written as an explicit product-formula, has been stated independently by George Andrews and David Robbins around 1983. We present a proof of this long-standing conjecture.

Edited by DALE PURVES GEORGE J . AUGUSTINE DAVID FITZPATRICK WILLIAM C . HALL ANTHONY - SAMUEL

Sub-Birkhoff

A fundamental result in rewriting is : E |= s ≈ t ⇐⇒1 E ` s = t ⇐⇒2 s↔E t 1. is Birkhoff’s theorem expressing that semantic consequence (|=) coincides with syntactic consequence (`). 2. expresses that equality in equational logic (=) coincides with convertibility in rewriting (↔∗), a property known as logicality. We show that the result can be extended to hold for several sub-equational logics ...

Topological Birkhoff

One of the most fundamental mathematical contributions of Garrett Birkhoff is the HSP theorem, which implies that a finite algebra B satisfies all equations that hold in a finite algebra A of the same signature if and only if B is a homomorphic image of a subalgebra of a finite power of A. On the other hand, if A is infinite, then in general one needs to take an infinite power in order to obtai...