Related papers: Numerical computations in cobordism categories

The sets of primitive foms may be decomposed into some Galois conjugacy classes. The purpose of this paper is to write down all of such classes with cardinal 1 or 2, explicitly in terms of some Eisenstein series, for level 1,2,3,4,6,8,9.…

We extend our investigation of $2$-determinants, which we defined in a previous paper. For a linear homogenous recurrence of the second order, we consider relations between different sequences satisfying the same linear homogeneous…

Let $n=4k+1$ and $k\geq 4$. We show that there exists maximal commutative subalgebras (with respect to inclusion) of dimension less that $3\cdot 2^{n-2}$.

Unitary metaplectic representations of the group $SL_2(\mathbb{Z}_{2^n})$ are necessary to describe the evolution of $2^n$-dimensional quantum systems, such as systems involving $n$ qubits. It is shown that in order for the metaplectic…

The branching functions of the affine superalgebra $sl(2/1)$ characters into characters of the affine subalgebra $sl(2)$ are calculated for fractional levels $k=1/u-1$, u positive integer. They involve rational torus $A_{u(u-1)}$ and…

For pairs of knots K and J in the three-sphere, we consider the set of four-tuples of integers (g,x,y,z) for which there is a cobordism from K to J of genus g having x, y, and z, critical points of index 0, 1, and 2, respectively. We…

We count the number of occurrences of certain patterns in given words. We choose these words to be the set of all finite approximations of a sequence generated by a morphism with certain restrictions. The patterns in our considerations are…

We explore potential uses of physics formulated in Kleinian (i.e., $2+2$) signature spacetimes as a tool for understanding properties of physics in Lorentzian (i.e., $3+1$) signature. Much as Euclidean (i.e., $4+0$) signature quantities can…

A conjecture of N. Terai states that for any integer $k>1$, the equation $x^2+(2k-1)^y =k^z$ has only one solution, namely, $(x, y, z) = (k-1, 1, 2).$ Using the structure of class groups of binary quadratic forms, we prove the conjecture…

Using a polylogarithmic identity, we express the values of $\zeta$ at odd integers $2n+1$ as integrals over unit $n-$dimensional hypercubes of simple functions involving products of logarithms. We also prove a useful property of those…

We construct a family of unoriented 2-dimensional cobordism theories parametrized by certain triples of sequences. We also prove that some specializations of these sequences yield equivalences with an exterior product of Deligne categories.…

It is known that for an arbitrary positive integer \(n\) the sequence \(S(x^n)=(1^n, 2^n, \ldots)\) is complete, meaning that every sufficiently large integer is a sum of distinct \(n\)th powers of positive integers. We prove that every…

The approach of Berezin to the quantization of so(n,2) via generalized coherent states is considered in detail. A family of n commuting observables is found in which the basis for an associated Fock-type representation space is expressed.…

Let $a,b$ and $n$ be positive integers with $a>b$. In this note, we prove that $$(2bn+1)(2bn+3){2bn \choose bn}\bigg|3(a-b)(3a-b){2an \choose an}{an\choose bn}.$$ This confirms a recent conjecture of Amdeberhan and Moll.

For every $n = 2^k > 8$ there exist exactly $[(k+1)/2]$ mutually nonequivalent $Z_4$-linear extended perfect codes with distance 4. All these codes have different ranks.

This is an announcement of certain rationality results for the critical values of the degree-2n L-functions attached to GL(1) $\times$ SO(n, n) over $\mathbb Q$ for an even positive integer n. The proof follows from studying the rank-one…

We count the number of subsets of $\{1,2,\cdots,n\}$ under different conditions and study the sequence obtained as we let $n$ increase.

We show that the decidability of the first-order theory of the language that combines Boolean algebras of sets of uninterpreted elements with Presburger arithmetic operations. We thereby disprove a recent conjecture that this theory is…

The odd part of 2^e! as e approaches infinity leads to a 2-adic integer z. The bits of z were publicized in OEIS-A359349, where two conjectures were made, relevant to computing z. We prove both of those conjectures. A second 2-adic integer,…

We define Collatz representations for a subset of rational numbers and prove that each real number \( x \notin (-1,1) \) can be approximated arbitrarily well by rational numbers which have only \( 2 \)'s and \( 1 \)'s in their Collatz…