Equality holds if and only if A consists of all r-subsets containing some fixed i ∈ [n]. What happens if, instead of demanding that A ⊂ [n] be intersecting, we demand that |x∩ y| is odd for any two distinct x, y ∈ A? How large can |A| be? It turns out that the answer depends heavily on whether r is even or odd. If r is odd, we can take A to be the family of all r-sets containing 1 and (r − 1)/2...

I comment on the above paper(s) discussing the issue of non-ultralocality for GinspargWilson fermionic actions. The purpose of this note is to point out that the new claim in “v3” (Feb 24, 2000), alleging the proof of non-ultralocality for “all Ginsparg-Wilson fermions”, might not be substantiated. The remarkable evolution of versions of this paper is put in context with the literature existing...

Operator cutoff regularization based on the original Schwinger's proper-time formalism is examined. By constructing a regulating smearing function for the proper-time integration, we show how this regularization scheme simulates the usual momentum cutoff prescription yet preserves gauge symmetry even in the presence of the cutoff scales. Similarity between the operator cutoff regularization and...