14 papers
How to pick your team with no size restriction
Hiranya Kishore Dey
Settling a problem raised by Eccles in 2015, Narayanan in 2026 considers a two-player game in which two captains alternately select players while the opponent decides to which team…
Group Structure from Subgroup and Cyclic Subgroup Counts
Angsuman Das, Hiranya Kishore Dey, Cesar Galindo +1
For a finite group \(G\), let \(\sub(G)\) be the number of subgroups of \(G\), let \(\cyc(G)\) be the number of cyclic subgroups, and let \(π(G)\) be the number of distinct prime d…
-analogues of Fisher's inequality and oddtown theorem
Hiranya Kishore Dey
A classical result in design theory, known as Fisher's inequality, states that if every pair of clubs in a town shares the same number of members, then the number of clubs cannot e…
A descent-excedance correspondence in colored permutation groups
Hiranya Kishore Dey, Umesh Shankar, Sivaramakrishnan Sivasubramanian
It is well known that descents and excedances are equidistributed in the symmetric group. We show that the descent and excedance enumerators, summed over permutations with a fixed…
Sign-balance of excedances over mod-k-alternating permutations and gamma-positivity
Hiranya Kishore Dey, Iswar Mahato
A permutation is called mod-k-alternating if its entries are restricted to having the same remainder as the index, modulo some integer In this paper, we find the sign-b…
How large is the character degree sum compared to the character table sum for a finite group?
Arvind Ayyer, Hiranya Kishore Dey, Digjoy Paul
In 1961, Solomon gave upper and lower bounds for the sum of all the entries in the character table of a finite group in terms of elementary properties of the group. In a different…