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Songpon Sriwongsa

Publications and source records attributed to Songpon Sriwongsa.

At least 19 recordsLinked to original sources
arXiv2026

Arithmetic exceptionality of Lattès maps

Let $\mathbb{F}_q$ denote a finite field of order $q$. A rational function $r(x)\in \mathbb{Q}(x)$ is said to be arithmetically exceptional if it induces a permutation on $\mathbb{P}^1(\mathbb{F}_p)$ for infinitely many primes $p$. Based on some computational results, Odabaş conjectured that for each $k\in \mathbb{N}$, the $k$-th Lattès map attached to an elliptic curve $E/\mathbb{Q}$ is arithmetically exceptional if and only if $E$ has no $k$-torsion point whose $x$-coordinate is rational. In this paper, we prove that this conjecture is true for any elliptic curve $E/\mathbb{Q}$ having complex multiplication by an imaginary quadratic field other than $\mathbb{Q}(\sqrt{-11}).$ On the other hand, we show that the conjecture becomes invalid if $E$ has CM by $\mathbb{Q}(\sqrt{-11})$ and $6\mid k$. Partial results for non-CM elliptic curves are also given.

math.NT↗
arXiv2026

Compressed sensing matrices from orthogonal spaces over finite fields of odd characteristic

In this paper, we construct deterministic matrices from subspaces of orthogonal spaces over finite fields of odd characteristic and investigate their applicability to compressed sensing. The construction is based on incidence relations among three types of subspaces, yielding families of matrices with explicitly computable dimensions and coherence. Using coherence-based estimates, we establish sufficient conditions under which these matrices satisfy the Restricted Isometry Property for prescribed sparsity levels. We also provide numerical comparisons with DeVore's deterministic construction to illustrate the trade-off between the number of measurements, coherence, and sparse recovery guarantees.

cs.IT↗
arXiv2026

Quantum fractional revival on zero-divisor graphs over $\mathbb{Z}_n$

In this paper, we characterize the existence of perfect state transfer (PST) and fractional revival in continuous-time quantum walks on the zero-divisor graph $Γ(\mathbb{Z}_n)$. By using the canonical equitable partition of $Γ(\mathbb{Z}_n)$ induced by the proper divisors of $n$, we derive a sufficient condition on $n$ for PST to occur between a pair of vertices. We show that fractional revival is restricted to cells of size $2$ within the equitable partition. Furthermore, assuming $-1$ is not an eigenvalue of the quotient spectrum, we establish that two vertices in $Γ(\mathbb{Z}_n)$ are strongly cospectral if and only if they form a cell of size $2$ within the equitable partition that is either a set of false twins or true twins. Finally, we provide a characterization of fractional revival on bipartite $Γ(\mathbb{Z}_n)$ and prove the non-existence of fractional revival on $Γ(\mathbb{Z}_{p^2q})$.

math.CO↗
arXiv2026

On solvable Lie algebras of small breadth

The concept of breadth has been used in the classification of p-groups and nilpotent Lie algebras. In this paper, we investigate this notion for finite-dimensional solvable Lie algebras. Our main focus is to characterize solvable Lie algebras of breadth less than or equal to 2. More importantly, we provide a complete classification of such Lie algebras that are pure and nonnilpotent over the complex numbers.

math.RA↗
arXiv2026

Quantum fractional revival on unitary Cayley graphs over finite commutative rings

In this paper, we investigate the existence of quantum fractional revival in unitary Cayley graphs over finite commutative rings with identity. We characterize all finite local rings that permit quantum fractional revival in their unitary Cayley graphs. Additionally, we present results for the case of finite commutative rings, as they can be expressed as products of finite local rings.

math.RA↗
arXiv2025

Non-commuting graphs of projective spaces over central quotients of Lie algebras

Let $L$ be a finite-dimensional non-abelian Lie algebra with the center $Z(L)$. In this paper, we define a non-commuting graph associated with $L$ as the graph whose vertex set is the projective space of the quotient algebra $L/Z(L)$, and two vertices $span \{ x + Z(L) \}$ and $span \{ y + Z(L) \}$ are adjacent if $x$ and $y$ do not commute under the Lie bracket of $L$. We present several theoretical properties of this graph. For certain classes of Lie algebras, we show that if the non-commuting graphs from two Lie algebras are isomorphic, then these Lie algebras themselves must be isomorphic. Furthermore, we discuss a relation between graph isomorphisms between non-commuting graphs of Lie algebras over finite fields and the size of the algebras.

math.RA↗
arXiv2025

A recursion formula for Branching from $\mathfrak{sl}_n$ to $\mathfrak{sl}_2$ subalgebras

For any representation of a complex simple Lie algebra $\mathfrak{sl}_n$, one problem of branching rules to $\mathfrak{sl}_2$-subalgebra is to determine the multiplicity of each irreducible component. In this paper, we derive a recursion formula of such multiplicities by restricting a certain tensor representation in two ways, in which the Pieri's rule is involved. We also investigate branching rules for fundamental representations as they are initial conditions of the recursion formula.

math.RT↗
arXiv2024

Classical orthogonal decomposition of a modular $\mathfrak{sl}_n$

An orthogonal decomposition problem of Lie algebras over the complex numbers has been studied since the 1980s. It has many applications and relations to other areas of mathematics and sciences. In this paper, we consider this decomposition problem over a field of prime characteristic. We define a classical orthogonal decomposition of a modular Lie algebra and construct it for $\mathfrak{sl}_n$ under certain sufficient conditions. Additionally, we provide more detailed analysis of the problem when $n = 2$ and $3$.

math.RA↗
arXiv2023

More on characteristic polynomials of Lie algebras

In recent years, the notion of characteristic polynomial of representations of Lie algebras has been widely studied. This paper provides more properties of these characteristic polynomials. For simple Lie algebras, we characterize the linearization of characteristic polynomials. Additionally, we characterize nilpotent Lie algebras via characteristic polynomials of the adjoint representation.

math.RT↗
arXiv2023

A dynamical system proof of Niven's theorem and its extensions

Niven's theorem asserts that $\{\cos(rπ) \mid r\in \mathbb{Q}\}\cap \mathbb{Q}=\{0,\pm 1,\pm 1/2\}.$ In this paper, we use elementary techniques and results from arithmetic dynamics to obtain an algorithm for classifying all values in the set $\{\cos(rπ) \mid r\in \mathbb{Q}\}\cap K$, where $K$ is an arbitrary number field.

math.NT↗
arXiv2022

On Automorphism Groups of Idempotent Evolution Algebras

We study the automorphism group of an idempotent evolution algebra, show that any finite group can be the automorphism group of an evolution algebra, and describe certain evolution algebras with given automorphism groups. In particular, we classify $n$-dimensional idempotent evolution algebras whose automorphism group is isomorphic to the symmetric group $S_n$, and classify idempotent evolution algebras with maximal diagonal automorphism subgroups.

math.RA↗
arXiv2021

Quasi-strongly regular graphs of grade three with diameter two

A quasi-strongly regular graph of grade $p$ with parameters $(n, k, a; c_1, \ldots, c_p)$ is a $k$-regular graph of order $n$ such that any two adjacent vertices share $a$ common neighbours and any two non-adjacent vertices share $c_{i}$ common neighbours for some $1 \leq i \leq p$. This is a generalization of a strongly regular graph. In this paper, we focus on strictly quasi-strongly regular graphs of grade $3$ with $c_i = k - i$ for $i = 1, 2, 3$. The main result is to show the sharp bounds of order $n$ for a given $k \geq 4$. Furthermore, by this result, we characterize all of these graphs whose $n$ satisfies upper or lower bounds.

math.CO↗
arXiv2020

Hilbert series of typical representations for Lie superalgebras

Let g be a basic classical Lie superalgebra over C. In the case of a typical weight whose every nonnegative integer multiple is also typical, we compute a closed form for the Hilbert series whose coefficients encode the dimensions of finite-dimensional irreducible typical g-representations. We give a formula for this Hilbert series in terms of elementary symmetric polynomials and Eulerian polynomials. Additionally, we show a simple closed form in terms of differential operators.

math.RT↗
arXiv2020

Branching from the General Linear Group to the Symmetric Group and the Principal Embedding

Let S be a principally embedded sl_2 subalgebra in sl_n for n > 2. A special case of results of the third author and Gregg Zuckerman implies that there exists a positive integer b(n) such that for any finite-dimensional irreducible sl_n representation, V, there exists an irreducible S-representation embedding in V with dimension at most b(n). In a 2017 paper (joint with Hassan Lhou), they prove that b(n)=n is the sharpest possible bound, and also address embeddings other than the principal one. These results concerning embeddings may by interpreted as statements about plethysm. Then, a well known result about these plethysms can be interpreted as a "branching rule". Specifically, a (finite dimensional) representation of GL(n,C) will decompose into irreducible representations of the symmetric group when it is restricted to the subgroup consisting of permutation matrices. The question of which irreducible representations of the symmetric group occur with positive multiplicity is the topic of this paper, applying the previous work of Lhou, Zuckerman, and the third author.

math.RT↗
arXiv2019

Orthogonal graphs modulo power of 2

In this work, we define an orthogonal graph on the set of equivalence classes of $(2ν+ δ)-$tuples over $\mathbb{Z}_{2^n}$ where $n$ and $ν$ are positive integers and $δ= 0, 1$ or $2$. We classify our graph if it is strongly regular or quasi-strongly regular and compute all parameters precisely. We show that our graph is arc transitive. The automorphisms group is given and the chromatic number of the graph except when $δ= 0$ and $ν$ is odd is determined. Moreover, we work on subconstituents of this orthogonal graph.

math.CO↗