Counting Toroidal Binary Arrays, II
نویسندگان
چکیده
We derive formulas for (i) the number of distinct toroidal n × n binary arrays, allowing rotation of rows and/or columns as well as matrix transposition, and (ii) the number of distinct toroidal n × n binary arrays, allowing rotation and/or reflection of rows and/or columns as well as matrix transposition.
منابع مشابه
Counting Toroidal Binary Arrays
A formula for the number of toroidal m × n binary arrays, allowing rotation of the rows and/or the columns but not reflection, is known. Here we find a formula for the number of toroidal m × n binary arrays, allowing rotation and/or reflection of the rows and/or the columns.
متن کاملCounting BPS Blackholes in Toroidal Type II String Theory
We derive a U-duality invariant formula for the degeneracies of BPS multiplets in a D1-D5 system for toroidal compactification of the type II string. The elliptic genus for this system vanishes, but it is found that BPS states can nevertheless be counted using a certain topo-logical partition function involving two insertions of the fermion number operator. This is possible due to four extra to...
متن کاملCounting Non-Isomorphic Chord Diagrams
Different formulas counting families of non isomorphic chord diagrams are given : planar and toroidal ones and those of maximal genus. These formulas are obtained establishing results on the structure of the automorphism group of diagrams of a given genus.
متن کاملCounting unlabelled toroidal graphs with no K33-subdivisions
We provide a description of unlabelled enumeration techniques, with complete proofs, for graphs that can be canonically obtained by substituting 2-pole networks for the edges of core graphs. Using structure theorems for toroidal and projectiveplanar graphs containing no K3,3-subdivisions, we apply these techniques to obtain their unlabelled enumeration.
متن کاملCounting Parameterized Border Arrays for a Binary Alphabet
The parameterized pattern matching problem is a kind of pattern matching problem, where a pattern is considered to occur in a text when there exists a renaming bijection on the alphabet with which the pattern can be transformed into a substring of the text. A parameterized border array (p-border array) is an analogue of a border array of a standard string, which is also known as the failure fun...
متن کامل