### Table 2 References [A] G.E. Andrews, The theory of partitions, Addison-Wesley, 1976. [B] R.E. Borcherds, Vertex algebras, Kac-Moody algebras and the Monster, Proc. Natl. Acad. Sci. USA 83 (1986), 3068-3071. [Ber] A. Berkovich, Fermionic counting of RSOS-states and Virasoro character formulas for the unitary minimal series M( ; + 1): Exact results, Bonn preprint;hep-th/9403073. [BLS] P. Bouwknegt, A. Ludwig and K. Schoutens, Spinon bases, Yangian symmetry and fermionic representations of Virasoro characters in conformal eld theory, preprint USC-94/9, PUPT-1469, hep-th/9406020.

in Combinatorial constructions of modules for infinite-dimensional Lie algebras, I. Principal subspace.

"... In PAGE 5: ...7) (x 2(mr(1) 2 ;2) x 2(mr(2) 2 +1;2)x2 2(mr(2) 2 ;2) x2 2(m1;2) x 1(mr(1) 1 ;1) x 1(mr(2) 1 +1;1)x2 1(mr(2) 1 ;1) x2 1(m1;1) mp;i 2 r(2) i?1 + r(2) i?1 ? 2 ? N for 1 p r(2) i ; mp+1;i mp;i ? 4 for 1 p lt; r(2) i ; i = 1; 2; mp;i 2 r(1) i?1 ? 2r(2) i ? 1 ? N for r(2) i lt; p r(1) i ; mp+1;i mp;i ? 2 for r(2) i lt; p lt; r(1) i ; i = 1; 2 9 gt; gt; gt; gt; gt; = gt; gt; gt; gt; ; ; where r(1) 0 = r(2) 0 := 0: For an explicit list of some basis elements with low enegies, see Example 5.1, Section 5 and the corresponding Table2 in the Appendix. (The quasi- particle monomial basis for g = sl(n + 1; C ) and level k highest weight ^ = k0 ^ 0 + kj ^ j; k0 + kj = k; 1 j n; is given in De nition 5.... In PAGE 28: ...W (2^ 0): We shall denote for brevity the quasi-particle monomial xs0 2(s) xt0 1(t) by (ss0 2 : : : tt0 1): For the rst few energy levels (the eigenvalues of the scaling operator D under the adjoint action), we list in Table2 of the Appendix the elements of BW(2^ 0) of types (1; 2) and (2; 2): It is illuminating to have the entries in this truncation condition written down in terms of the color-dual-charge-type parameters r(t) i : Suppose np;i = s; 1 s k: Then r(1) i?1 X q=1 minfnp;i; nq;i?1g = r(1) i?1 X q=1 min fs; nq;i?1g = s Xt=1 r(t) i?1: (5.9) Since the number of quasi-particles of charge s and color i is r(s) i ? r(s+1) i ; the total \shift quot; due to the interaction between quasi-particles of colors i and i ? 1 is k X s=1(r(s) i ? r(s+1) i ) s Xt=1 r(t) i?1 = (5.... ..."

### Table 1. Symmetry

2000

"... In PAGE 11: ...6) is rather target-system independent. Second, it is easily realizable in RDF(S). Third, our approach for denoting symmetry is much sparser than its initital counterpart (4), because (7) is implicitly assumed as the agreed semantics for our schema definition. Following our strategy sketched in the previous subsection, these steps from RDF representation to axiom meaning are now summarized in Table1 . For easier under- standing, we will reuse this table layout also in the following subsection.... ..."

Cited by 25

### Table 1. Symmetry

2000

"... In PAGE 11: ...6) is rather target-system independent. Second, it is easily realizable in RDF(S). Third, our approach for denoting symmetry is much sparser than its initital counterpart (4), because (7) is implicitly assumed as the agreed semantics for our schema definition. Following our strategy sketched in the previous subsection, these steps from RDF representation to axiom meaning are now summarized in Table1 . For easier under- standing, we will reuse this table layout also in the following subsection.... ..."

Cited by 25

### Table 1. Symmetry

2000

"... In PAGE 12: ... Third, our approach for denoting symmetry is much sparser than its initital coun- terpart (4), because (7) is implicitly assumed as the agreed semantics for our schema definition. Following our strategy sketched in the previous subsection, these steps from RDF representation to axiom meaning are now summarized in Table1 . For easier under- standing, we will reuse this table layout also in the following subsection.... ..."

Cited by 5

### Table 1. Symmetry

"... In PAGE 12: ... Third, our approach for denoting symmetry is much sparser than its initital coun- terpart (4), because (7) is implicitly assumed as the agreed semantics for our schema definition. Following our strategy sketched in the previous subsection, these steps from RDF representation to axiom meaning are now summarized in Table1 . For easier under- standing, we will reuse this table layout also in the following subsection.... ..."

### Table 3: test for symmetry

### Table 3: Symmetry Detection Times.

1994

"... In PAGE 14: ... The larger di erences are due to di erent numbers of iterations to reach convergence. Table3 gives the times required to run the symmetry check once the BDDs are built. For our method, this corresponds to the time required by the one pass of sifting done after the BDDs are built for all primary outputs.... ..."

Cited by 52

### Table 2 Scope of symmetry programs

1996

"... In PAGE 26: ... Table2 cont. Scope of symmetry programs Name System Developer(s) Point General.... ..."