---------- Forwarded message ----------
From: Miklos Bona <bona@ufl.edu>
Date: Mon, Jan 13, 2014 at 2:57 PM
Subject: [E-JC] Editor Decision: Using Functional Equations to Enumerate
1324-avoiding Permutations
To: Brian Nakamura <bnaka@math.rutgers.edu>
Cc: Andre Kundgen <akundgen@csusm.edu>


Dear Brian,

We regret to inform you that we have decided not to proceed with publication
of your submission "Using Functional Equations to Enumerate 1324-avoiding
Permutations" to The Electronic Journal of Combinatorics.

Our journal receives a great number of high quality submissions every year,
and we can only publish those few that in our estimation have the most
substantial mathematical depth, importance, originality and interest to our
readers.

We thank you for submitting your paper to our journal. We would be happy to
consider future papers of yours for publication.

Miklos Bona
University of Florida
bona@UFL.edu

------------------------------------------------------
Reviewer A:

PREAMBLE:  It is not easy for a referee to base her/his rejection of a
paper based primarily on the fact that, in their opinion, the paper is not
of the highest quality.  I was asked by the editorial staff to use what
appear to be the "new" EJC criteria, as follows: Please apply very high
standards, those of the best journals in combinatorics.  A paper must be
more than just publishable to meet our standards.  In particular, it would
be useful if you could comment on the importance of the research in this
paper and not just look at it for correctness.

STRATEGY I EMPLOYED:  1. I browsed through the published papers in the last
two issues of EJC, using them as representatives of the quality now desired
by the journal. 2. I fully believe the results are probably correct but did
not go derivations of the rigorous functional equations line by line.

REASON FOR MY RECOMMENDATION:

The determination of the Stanley Wilf constant for 1324 avoiding
permutations is the holy grail in the area of pattern avoidance, with key
work by Bona, Claesson et al, and (indirectly) even the new paper of Fox.
 The functional equation schemes with many catalytical variables employed
by the authors is sufficient to allow, at the current level of computer
power, to uncover six new values of av(1324), that support the conjecture
that the SW limit is no less than ~10.45.  When the number of inversions is
incorporated into the analysis, there is slight evidence to support a
conjecture of Claesson et al.  The functional equations allow one,
moreover, to gain slightly more limited understanding of the case r>=3
(multiple occurrences).  There is no punch line, however, and no definitive
proof in the area, and so I rated this work as high-class experimental math
(interpreted in a broad sense).

I am not sure where to recommend the authors resubmit.  Adv. Appl. Math.
has been the standard place for results of this type, but perhaps the people
in the PP community might want to explore "Experimental Mathematics" or
journals that specialize in functional equations.
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