10 citations · 51 across the 41 of their papers we have counts for
14 papers · 1 filter
Dyck paths on colored lattices
Manjil P. Saikia
Fried recently enumerated Dyck paths having equally many black and white cells below them, for the chessboard coloring (Narayana numbers) and the column-alternating coloring (Fuss-…
Hook Length Biases in -Core Partitions
Nayandeep Deka Baruah, Hirakjyoti Das, Pankaj Jyoti Mahanta +1
Recently, the theory of hook length biases has emerged as a prominent research topic. Led by Ballantine, Burson, Craig, Folsom, and Wen [\textit{Res. Math. Sci.}, 2023], hook lengt…
Hook-Length Biases in -regular partitions
Manjil P. Saikia, Prabal Talukdar
Recently, there has been a lot of work on combinatorial inequalities related to hook-lengths in -regular partitions. In this short note, we give a proof using generating functio…
Arithmetic properties of -Schur overpartitions
Mohammed L. Nadji, Manjil P. Saikia, James A. Sellers
In a recent work, Nadji and Ahmia introduced the -Schur overpartitions as an overpartition analogue for -Schur partitions, which generalizes the classical Schur's partitions…
Symmetric Domino Tilings of Aztec Diamonds
Pravakar Paul, Manjil P. Saikia
In this paper, we give inductive sum formulas to calculate the number of diagonally symmetric, and diagonally \& anti-diagonally symmetric domino tilings of Aztec Diamonds. As a by…
Combinatorial Proofs of Some Results of Andrews and El Bachraoui
Pankaj Jyoti Mahanta, Manjil P. Saikia
Recently, Andrews and El Bachraoui (2024) proved three very interesting -series identities, from which three simple looking identities involving certain restricted partitions in…
A Novel Approach to Counting Perfect Matchings of Graphs
Pravakar Paul, Manjil P. Saikia
We build a new perspective to count perfect matchings of a given graph. This idea is motivated by a construction on the relative cohomology group of surfaces. As an application of…
Extensions of some results of Jovovic and Dhar
Pankaj Jyoti Mahanta, Manjil P. Saikia
We look at extensions of formulas given by Jovovic and recently proved by Dhar on integer partitions where the smallest part occurs at least times and on integer partitions wit…
Refinement of some partition identities of Merca and Yee
Pankaj Jyoti Mahanta, Manjil P. Saikia
Recently, Merca and Yee proved some partition identities involving two new partition statistics. We refine these statistics and generalize the results of Merca and Yee. We also cor…
Parity biases in partitions and restricted partitions
Koustav Banerjee, Sreerupa Bhattacharjee, Manosij Ghosh Dastidar +2
Let (resp. ) denote the number of partitions of with more odd parts (resp. even parts) than even parts (resp. odd parts). Recently, Kim, Kim, and Lovejoy p…
Some New and Old Gibonacci Identities
Pankaj Jyoti Mahanta, Manjil P. Saikia
We present a different combinatorial interpretations of Lucas and Gibonacci numbers. Using these interpretations we prove several new identities, and simplify the proofs of several…
A family of lacunary recurrences for Lucas Numbers
Pankaj Jyoti Mahanta, Manjil P. Saikia
We prove an infinite family of lacunary recurrences for the Lucas numbers using combinatorial means.
Refined Enumeration of Symmetry Classes of Alternating Sign Matrices
Ilse Fischer, Manjil P. Saikia
We prove refined enumeration results on several symmetry classes as well as related classes of alternating sign matrices with respect to classical boundary statistics, using the si…
Enumeration of Domino Tilings of an Aztec Rectangle with boundary defects
Manjil P. Saikia
Helfgott and Gessel gave the number of domino tilings of an Aztec Rectangle with defects of size one on the boundary of one side. In this paper we extend this to the case of domino…