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of 109
pro vyhledávání: '"Staic, Mihai D."'
In this paper we study an equivalence relation defined on the set of cycle-free $d$-partitions of the complete graph $K_{2d}$. We discuss a conjecture which states that this equivalence relation has only one equivalence class, and show that the conje
Externí odkaz:
http://arxiv.org/abs/2407.13959
Autor:
Staic, Mihai D.
In this paper we introduce the $r$-equilibrium problem and discuss connections to the map $det^{S^r}$. The case $r=2$ is an application of Newton's third law of motion, while $r=3$ deals with equilibrium of torque-like forces.
Comment: 11 pages,
Comment: 11 pages,
Externí odkaz:
http://arxiv.org/abs/2405.10407
Autor:
Lippold, Steven R., Staic, Mihai D.
In this paper we show the existence of a nontrivial linear map $det^{S^3}:V_d^{\otimes\binom{3d}{3}}\to k$ with the property that $det^{S^3}(\otimes_{1\leq i
Externí odkaz:
http://arxiv.org/abs/2211.10375
Autor:
Staic, Mihai D.
Using the $det^{S^2}$ map from [5], we introduce the notion of $S^2$-rank of a matrix of type $d\times \frac{s(s-1)}{2}$. As an application, we show that the conditional probability matrix associated to two random variables has the $S^2$-rank equal t
Externí odkaz:
http://arxiv.org/abs/2205.02183
Autor:
Staic, Mihai D.
In this paper we show that for a vector space $V_d$ of dimension $d$ there exists a linear map $det^{S^2}:V_d^{\otimes d(2d-1)}\to k$ with the property that $det^{S^2}(\otimes_{1\leq i
Externí odkaz:
http://arxiv.org/abs/2205.02178
Autor:
Lippold, Steven R., Staic, Mihai D.
Publikováno v:
In Linear Algebra and Its Applications 15 May 2024 689:1-33
Autor:
Lippold, Steven R., Staic, Mihai D.
In this paper we introduce a determinant-like map $det^{S^3}$ and study some of its properties. For this we define a graded vector space $\Lambda^{S^3}_V$ that has similar properties with the exterior algebra $\Lambda_V$ and the exterior GSC-operad $
Externí odkaz:
http://arxiv.org/abs/2107.13609
In this paper we prove the case $dim(V_3)=3$ of a conjecture about the exterior operad ${\Lambda}^{S^2}_{V_d}$. For this we introduce a collection of natural involutions on the set of homogeneous cycle-free $d$-partitions of the complete graph $K_{2d
Externí odkaz:
http://arxiv.org/abs/2102.09422
Autor:
Staic, Mihai D., Van Grinsven, Jacob
We discuss properties of the $det^{S^2}$ map, present a few explicit computations, and give a geometrical interpretation for the condition $det^{S^2}((v_{i,j})_{1\leq i Comment: 5 pages, all comments are welcome
Externí odkaz:
http://arxiv.org/abs/2009.13641
Autor:
Staic, Mihai D
In this paper we present a construction which is a generalization of the exterior algebra of a vector space $V$. We show how this fits in the language of operads, discuss some properties, and give explicit computations for the case $dim(V)=2$.
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Externí odkaz:
http://arxiv.org/abs/2002.00520