Báo cáo toán học: "A Plethysm Formula for pµ (x) ◦ hλ (x) William F Doran IV Department of Mathematics California Institute of Technology Pasadena, CA 91125" doc
... A Plethysm Formula for p
µ
(x) ◦ h
λ
(x)
William F. Doran IV
Department of Mathematics
California Institute of Technology
Pasadena, CA 91125
doran@ cco.caltech.edu
Submitted: ... gives a new formula for the plethysm of
power-sum symmetric functions and complete symmet-
ric functions. The form of the main result is that for
µ b and λ ...
... interpretation of the closed formula (10) for the number of con-
vex permutominoes. We remark that the expression of f
n
resembles the expression
(1) for the number c
n
of convex polyominoes of semi-perimeter ... a closed formula for the number of convex permu-
tominoes of size n. We reach this goal by providing a recursive generation of all
convex permutominoes o...
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... the formulae of
[4, 22], which appear as a byproduct of proofs or attempted proofs of certain conjectures
of [25]. Specifically, consider as in [22] FPL configurations in a triangle of the form of
Fig. ... ∅
Figure 4: Example of parameterization of the boundary conditions of FPLs in a triangle.
the connectivity of the ver tical external edges can be encoded into a link patte...
... for the
rest of the paper. For further background information on the properties of the symmetric
group, one can refer to the books of [9] and [17]. Section 3 gives the construction of the
diagram ... known formula for these elements.
Herein, we describe an explicit construction for two different families o f orthogonal
idempo tents in CH
0
(S
N
), one for each of the tw...
... columns. In Figure 1.c a
reverse SSYT of shape (4, 3, 3, 1)/(2, 2, 1) is shown.
2 A Bijective proof of Identity 1
In fact, we will give a bijective proof of the following rewriting of Identity ... principle-free bijective proof of Stanley’s hook-
content formula, Discrete Mathematics and Theoretical Computer Science (1998),
no. 3, 11–32.
[3]
, Another involution principle-free bi...
... than that of Ag/Si, 8.64 × 10
−
2 Ω cm
2
. It was found that Mg/Si was suitable for a
high-efficiency solar cell application.
Figure 3 shows the carrier lifetimes of Si wafers with different ... Å.
Figure 4. Dependence of reflectance on the Mg thickness and oxidation steps.
Figure 5. Effect of Mg thickness on the DIV of the processed solar cells.
Figure 6. Sun-V
oc...