The 2-adic Valuation of Plane Partitions and Totally Symmetric Plane Partitions
نویسندگان
چکیده
منابع مشابه
The 2-adic Valuation of Plane Partitions and Totally Symmetric Plane Partitions
This paper confirms a conjecture of Amdeberhan and Moll that the power of 2 dividing the number of plane partitions in an n-cube is greater than the power of 2 dividing the number of totally symmetric plane partitions in the same cube when n is even, and less when n is odd.
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We present multiresidue integral formulae for partial sums in the basis of link patterns of the polynomial solution to the level 1 Uq(ŝl2) quantum Knizhnik–Zamolodchikov equation at generic values of the quantum parameter q. These allow for rewriting and generalizing a recent conjecture [Di Francesco ’06] connecting the above to generating polynomials for weighted Totally Symmetric Self-Complem...
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In 2012, Blecher defined the combinatorial objects known as 1–shell totally symmetric plane partitions of weight n. He also proved that the generating function for f (n), the number of 1–shell totally symmetric plane partitions of weight n, is given by ∑
متن کاملThe Equivalence between Enumerating Cyclically Symmetric, Self-Complementary and Totally Symmetric, Self-Complementary Plane Partitions
We prove that the number of cyclically symmetric, self-complementary plane partitions contained in a cube of side 2n equals the square of the number of totally symmetric, self-complementary plane partitions contained in the same cube, without explicitly evaluating either of these numbers. This appears to be the first direct proof of this fact. The problem of finding such a proof was suggested b...
متن کاملPlane Partitions
Throughout our study of the enumeration of plane partitions we make use of bijective proofs to find generating functions. In particular, we consider bounded plane partitions, symmetric plane partitions and weak reverse plane partitions. Using the combinatorial interpretations of Schur functions in relation to semistandard Young tableaux, we rely on the properties of symmetric functions. In our ...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2012
ISSN: 1077-8926
DOI: 10.37236/2064