Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lattice points and simultaneous core partitions   We observe that for a and b relatively prime, the "abacus construction"
identifies the set of simultaneous (a,b)-core partitions with lattice points in
a rational simplex. Furthermore, many statistics on (a,b)-cores are piecewise
polynomial functions on this simplex. We apply these results to rational
Catalan combinatorics.
  Using Ehrhart theory, we reprove Anderson's theorem that there are
(a+b-1)!/a!b! simultaneous (a,b)-cores, and using Euler-Maclaurin theory we
prove Armstrong's conjecture that the average size of an (a,b)-core is
(a+b+1)(a-1)(b-1)/24. Our methods also give new derivations of analogous
formulas for the number and average size of self-conjugate (a,b)-cores.
  We conjecture a unimodality result for q rational Catalan numbers, and make
preliminary investigations in applying these methods to the (q,t)-symmetry and
specialization conjectures. We prove these conjectures for low degree terms and
when a=3, connecting them to the Catalan hyperplane arrangement and quadratic
permutation statistics.

22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph