10 papers
Dold-Gauss Congruences, Norm Descent, and Rational Rigidity
Hartosh Singh Bal
We develop a Witt--Hadamard calculus for Euler products that unifies the classical Gauss congruences with their modern refinement, the Dold congruences. Within this framework we pr…
Beyond Bass Collapse: New Irregular Edge-Space Invariants in Ihara Theory
Hartosh Singh Bal
Let \(G\) be a finite simple graph and let \(T\) be its Hashimoto operator on the directed-edge space. We show that edge reversal induces a canonical symmetric/antisymmetric splitt…
The Antisymmetric Line Graph
Hartosh Singh Bal
Let be a finite simple graph with oriented incidence matrix . The signed graph on edge set with adjacency matrix \[ A_{\mathcal A(G)}=D^{\mathsf T}D-2I \] is classica…
Perfecting the Line Graph
Hartosh Singh Bal
We study the doubled edge-stage lift \[ \HL'_2(G)=L(G\otimes K_2), \] the line graph of the canonical bipartite double cover of a graph \(G\). The natural involution \((u,v)\leftri…
Partition Frequency Moments: Modularity and Congruences
Hartosh Singh Bal
We study frequency moments of partition statistics arising from Euler products via a transform that expresses the moment generating functions as…
The Partition-Frequency Enumeration Matrix
Hartosh Singh Bal, Gaurav Bhatnagar
We develop a calculus that gives an elementary approach to enumerate partition-like objects using an infinite upper-triangular number-theoretic matrix. We call this matrix the Part…