Combinatorial computation of combinatorial formulas for knot invariants
نویسندگان
چکیده
منابع مشابه
Combinatorial Formulas for Cohomology of Knot Spaces
We develop homological techniques for finding explicit combinatorial formulas for finite-type cohomology classes of spaces of knots in R, n ≥ 3, generalizing the Polyak—Viro formulas [9] for invariants (i.e., 0-dimensional cohomology classes) of knots in R. As the first applications, we give such formulas for the (reduced mod 2) generalized Teiblum—Turchin cocycle of order 3 (which is the simpl...
متن کاملGoussarov-polyak-viro Combinatorial Formulas for Finite Type Invariants
Goussarov, Polyak, and Viro proved that finite type invariants of knots are “finitely multi-local”, meaning that on a knot diagram, sums of quantities, defined by local information, determine the value of the knot invariant ([2]). The result implies the existence of Gauss diagram combinatorial formulas for finite type invariants. This article presents a simplified account of the original approa...
متن کاملCombinatorial Maps with Normalized Knot
We consider combinatorial maps with fixed combinatorial knot numbered with augmenting numeration called normalized knot. We show that knot’s normalization doesn’t affect combinatorial map what concerns its generality. Knot’s normalization leads to more concise numeration of corners in maps, e.g., odd or even corners allow easy to follow distinguished cycles in map caused by the fixation of the ...
متن کاملCombinatorial Proofs of Addition Formulas
In this paper we give a combinatorial proof of an addition formula for weighted partial Motzkin paths. The addition formula allows us to determine the LDU decomposition of a Hankel matrix of the polynomial sequence defined by weighted partial Motzkin paths. As a direct consequence, we get the determinant of the Hankel matrix of certain combinatorial sequences. In addition, we obtain an addition...
متن کاملCombinatorial Addition Formulas and Applications
We derive addition formulas at the combinatorial level, that is equations of the form F (X1+ X2 + +Xk) = F (X1; X2; : : : ; Xk), where F = F (X) is a given combinatorial species and F is a species on k sorts of singletons X1; X2; : : : ; Xk; depending on F . General results are given in the case of a molecular species M = X=H. Speci c formulas are also presented in the cases of the species Ln o...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the Moscow Mathematical Society
سال: 2005
ISSN: 0077-1554,1547-738X
DOI: 10.1090/s0077-1554-05-00148-2